\psset{unit=0.45cm}
%
\pspicture(-15,-8.5)(15,8)
% The Young tableaux
% The grid for the skew Ferrers diagram:
% The horizontal lines:
\psline[linewidth=0.085,linecolor=gray](-11.6667,-2)(-8.55556,-2)
\psline[linewidth=0.085,linecolor=gray](-11.6667,-2.77778)(-8.55556,-2.77778)
\psline[linewidth=0.085,linecolor=gray](-12.4444,-3.55556)(-10.8889,-3.55556)
\psline[linewidth=0.085,linecolor=gray](-12.4444,-4.33333)(-10.8889,-4.33333)
\psline[linewidth=0.085,linecolor=gray](-13.2222,-5.11111)(-11.6667,-5.11111)
\psline[linewidth=0.085,linecolor=gray](-14,-5.88889)(-13.2222,-5.88889)
\psline[linewidth=0.085,linecolor=gray](-14,-6.66667)(-13.2222,-6.66667)
\psline[linewidth=0.085,linecolor=gray](-14,-7.44444)(-13.2222,-7.44444)
% The vertical lines:
\psline[linewidth=0.085,linecolor=gray](-14,-5.11111)(-14,-7.44444)
\psline[linewidth=0.085,linecolor=gray](-13.2222,-5.11111)(-13.2222,-7.44444)
\psline[linewidth=0.085,linecolor=gray](-12.4444,-4.33333)(-12.4444,-5.11111)
\psline[linewidth=0.085,linecolor=gray](-11.6667,-2.77778)(-11.6667,-5.11111)
\psline[linewidth=0.085,linecolor=gray](-10.8889,-2)(-10.8889,-4.33333)
\psline[linewidth=0.085,linecolor=gray](-10.1111,-2)(-10.1111,-2.77778)
\psline[linewidth=0.085,linecolor=gray](-9.33333,-2)(-9.33333,-2.77778)
\psline[linewidth=0.085,linecolor=gray](-8.55556,-2)(-8.55556,-2.77778)
\pspolygon[linewidth=0.2,linecolor=gray](-8.55556,-2)(-8.55556,-2.77778)(-10.8889,-2.77778)(-10.8889,-4.33333)(-11.6667,-4.33333)(-11.6667,-5.11111)(-13.2222,-5.11111)(-13.2222,-7.44444)(-14,-7.44444)(-14,-5.11111)(-13.2222,-5.11111)(-13.2222,-4.33333)(-12.4444,-4.33333)(-12.4444,-2.77778)(-11.6667,-2.77778)(-11.6667,-2)
% Young tableau labels:
% Row 1:
\rput(-11.2778,-2.38889){${\scriptstyle\mathbf 1}$}
\rput(-10.5,-2.38889){${\scriptstyle\mathbf 6}$}
\rput(-9.72222,-2.38889){${\scriptstyle\mathbf 6}$}
\rput(-8.94444,-2.38889){${\scriptstyle\mathbf 7}$}
% Row 2:
\rput(-12.0556,-3.16667){${\scriptstyle\mathbf 3}$}
\rput(-11.2778,-3.16667){${\scriptstyle\mathbf 3}$}
% Row 3:
\rput(-12.0556,-3.94444){${\scriptstyle\mathbf 6}$}
\rput(-11.2778,-3.94444){${\scriptstyle\mathbf 7}$}
% Row 4:
\rput(-12.8333,-4.72222){${\scriptstyle\mathbf 5}$}
\rput(-12.0556,-4.72222){${\scriptstyle\mathbf 7}$}
% Row 5:
\rput(-13.6111,-5.5){${\scriptstyle\mathbf 3}$}
% Row 6:
\rput(-13.6111,-6.27778){${\scriptstyle\mathbf 4}$}
% Row 7:
\rput(-13.6111,-7.05556){${\scriptstyle\mathbf 5}$}
% The grid for the skew Ferrers diagram:
% The horizontal lines:
\psline[linewidth=0.085,linecolor=gray](-6.66667,-2)(-3.55556,-2)
\psline[linewidth=0.085,linecolor=gray](-6.66667,-2.77778)(-3.55556,-2.77778)
\psline[linewidth=0.085,linecolor=gray](-7.44444,-3.55556)(-5.88889,-3.55556)
\psline[linewidth=0.085,linecolor=gray](-7.44444,-4.33333)(-5.88889,-4.33333)
\psline[linewidth=0.085,linecolor=gray](-8.22222,-5.11111)(-6.66667,-5.11111)
\psline[linewidth=0.085,linecolor=gray](-9,-5.88889)(-8.22222,-5.88889)
\psline[linewidth=0.085,linecolor=gray](-9,-6.66667)(-8.22222,-6.66667)
\psline[linewidth=0.085,linecolor=gray](-9,-7.44444)(-8.22222,-7.44444)
% The vertical lines:
\psline[linewidth=0.085,linecolor=gray](-9,-5.11111)(-9,-7.44444)
\psline[linewidth=0.085,linecolor=gray](-8.22222,-5.11111)(-8.22222,-7.44444)
\psline[linewidth=0.085,linecolor=gray](-7.44444,-4.33333)(-7.44444,-5.11111)
\psline[linewidth=0.085,linecolor=gray](-6.66667,-2.77778)(-6.66667,-5.11111)
\psline[linewidth=0.085,linecolor=gray](-5.88889,-2)(-5.88889,-4.33333)
\psline[linewidth=0.085,linecolor=gray](-5.11111,-2)(-5.11111,-2.77778)
\psline[linewidth=0.085,linecolor=gray](-4.33333,-2)(-4.33333,-2.77778)
\psline[linewidth=0.085,linecolor=gray](-3.55556,-2)(-3.55556,-2.77778)
\pspolygon[linewidth=0.2,linecolor=black](-3.55556,-2)(-3.55556,-2.77778)(-5.88889,-2.77778)(-5.88889,-4.33333)(-6.66667,-4.33333)(-6.66667,-5.11111)(-8.22222,-5.11111)(-8.22222,-7.44444)(-9,-7.44444)(-9,-5.11111)(-8.22222,-5.11111)(-8.22222,-4.33333)(-7.44444,-4.33333)(-7.44444,-2.77778)(-6.66667,-2.77778)(-6.66667,-2)
% Young tableau labels:
% Row 1:
\rput(-6.27778,-2.38889){${\scriptstyle\mathbf 6}$}
\rput(-5.5,-2.38889){${\scriptstyle\mathbf 6}$}
\rput(-4.72222,-2.38889){${\scriptstyle\mathbf 8}$}
\rput(-3.94444,-2.38889){${\scriptstyle\mathbf 8}$}
% Row 2:
\rput(-7.05556,-3.16667){${\scriptstyle\mathbf 5}$}
\rput(-6.27778,-3.16667){${\scriptstyle\mathbf 7}$}
% Row 3:
\rput(-7.05556,-3.94444){${\scriptstyle\mathbf 6}$}
\rput(-6.27778,-3.94444){${\scriptstyle\mathbf 8}$}
% Row 4:
\rput(-7.83333,-4.72222){${\scriptstyle\mathbf 4}$}
\rput(-7.05556,-4.72222){${\scriptstyle\mathbf 7}$}
% Row 5:
\rput(-8.61111,-5.5){${\scriptstyle\mathbf 3}$}
% Row 6:
\rput(-8.61111,-6.27778){${\scriptstyle\mathbf 7}$}
% Row 7:
\rput(-8.61111,-7.05556){${\scriptstyle\mathbf 8}$}
% The square grid with labels
% Square grid:
% The vertical lines:
\psline[linewidth=0.085,linecolor=lightgray](-15,0)(-15,7)
\psline[linewidth=0.085,linecolor=lightgray](-14,0)(-14,7)
\psline[linewidth=0.085,linecolor=lightgray](-13,0)(-13,7)
\psline[linewidth=0.085,linecolor=lightgray](-12,0)(-12,7)
\psline[linewidth=0.085,linecolor=lightgray](-11,0)(-11,7)
\psline[linewidth=0.085,linecolor=lightgray](-10,0)(-10,7)
\psline[linewidth=0.085,linecolor=lightgray](-9,0)(-9,7)
\psline[linewidth=0.085,linecolor=lightgray](-8,0)(-8,7)
\psline[linewidth=0.085,linecolor=lightgray](-7,0)(-7,7)
\psline[linewidth=0.085,linecolor=lightgray](-6,0)(-6,7)
\psline[linewidth=0.085,linecolor=lightgray](-5,0)(-5,7)
\psline[linewidth=0.085,linecolor=lightgray](-4,0)(-4,7)
\psline[linewidth=0.085,linecolor=lightgray](-3,0)(-3,7)
\psline[linewidth=0.085,linecolor=lightgray](-2,0)(-2,7)
\psline[linewidth=0.085,linecolor=lightgray](-1,0)(-1,7)
% The horizontal lines:
\psline[linewidth=0.085,linecolor=lightgray](-15,0)(-1,0)
\psline[linewidth=0.085,linecolor=lightgray](-15,1)(-1,1)
\psline[linewidth=0.085,linecolor=lightgray](-15,2)(-1,2)
\psline[linewidth=0.085,linecolor=lightgray](-15,3)(-1,3)
\psline[linewidth=0.085,linecolor=lightgray](-15,4)(-1,4)
\psline[linewidth=0.085,linecolor=lightgray](-15,5)(-1,5)
\psline[linewidth=0.085,linecolor=lightgray](-15,6)(-1,6)
\psline[linewidth=0.085,linecolor=lightgray](-15,7)(-1,7)
% Ray of labels:
\rput(-15,-1){${\scriptscriptstyle -7}$}
\rput(-14,-1){${\scriptscriptstyle -6}$}
\rput(-13,-1){${\scriptscriptstyle -5}$}
\rput(-12,-1){${\scriptscriptstyle -4}$}
\rput(-11,-1){${\scriptscriptstyle -3}$}
\rput(-10,-1){${\scriptscriptstyle -2}$}
\rput(-9,-1){${\scriptscriptstyle -1}$}
\rput(-8,-1){${\scriptscriptstyle 0}$}
\rput(-7,-1){${\scriptscriptstyle 1}$}
\rput(-6,-1){${\scriptscriptstyle 2}$}
\rput(-5,-1){${\scriptscriptstyle 3}$}
\rput(-4,-1){${\scriptscriptstyle 4}$}
\rput(-3,-1){${\scriptscriptstyle 5}$}
\rput(-2,-1){${\scriptscriptstyle 6}$}
\rput(-1,-1){${\scriptscriptstyle 7}$}
% The recolouring paths
\psline[linecolor=gray,linewidth=0.3,linearc=0.6](-1,7)(-1,6)(-2,6)(-2,5)(-4,5)(-4,7)(-2,7)
\psline[linecolor=gray,linewidth=0.3,linearc=0.6](-5,0)(-4,0)(-4,5)(-5,5)(-5,7)
\psline[linecolor=gray,linewidth=0.3,linearc=0.6](-7,0)(-7,2)(-6,2)(-6,0)
\psline[linecolor=gray,linewidth=0.3,linearc=0.6](-8,7)(-7,7)
\psline[linecolor=gray,linewidth=0.3,linearc=0.6](-9,7)(-9,6)(-8,6)(-8,5)(-7,5)(-7,4)(-8,4)(-8,5)(-9,5)(-9,6)(-10,6)(-10,4)(-9,4)(-9,0)
\psline[linecolor=gray,linewidth=0.3,linearc=0.6](-10,0)(-10,3)(-11,3)(-11,7)
\psline[linecolor=gray,linewidth=0.3,linearc=0.6](-11,0)(-11,2)(-12,2)(-12,3)(-13,3)(-13,2)(-12,2)(-12,0)
\psline[linecolor=gray,linewidth=0.3,linearc=0.6](-15,0)(-15,7)(-14,7)
% The lattice paths corresponding to T1
% Lattice paths:
% Path 1:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](-5.1,0.1)(-4.1,0.1)(-4.1,5.1)(-3.1,5.1)(-2.1,5.1)(-2.1,6.1)(-1.1,6.1)(-1.1,7.1)
% Path 2:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](-7.1,0.1)(-7.1,2.1)(-6.1,2.1)(-5.1,2.1)(-5.1,7.1)
% Path 3:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](-8.1,0.1)(-8.1,5.1)(-7.1,5.1)(-7.1,6.1)(-6.1,6.1)(-6.1,7.1)
% Path 4:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](-10.1,0.1)(-10.1,4.1)(-9.1,4.1)(-9.1,6.1)(-8.1,6.1)(-8.1,7.1)
% Path 5:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](-12.1,0.1)(-12.1,2.1)(-11.1,2.1)(-11.1,7.1)
% Path 6:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](-13.1,0.1)(-13.1,3.1)(-12.1,3.1)(-12.1,7.1)
% Path 7:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](-14.1,0.1)(-14.1,4.1)(-13.1,4.1)(-13.1,7.1)
% Lattice path labels:
% Path 1:
\rput(-4.6,0.35){${\scriptscriptstyle 1}$}
\rput(-3.6,5.35){${\scriptscriptstyle 6}$}
\rput(-2.6,5.35){${\scriptscriptstyle 6}$}
\rput(-1.6,6.35){${\scriptscriptstyle 7}$}
% Path 2:
\rput(-6.6,2.35){${\scriptscriptstyle 3}$}
\rput(-5.6,2.35){${\scriptscriptstyle 3}$}
% Path 3:
\rput(-7.6,5.35){${\scriptscriptstyle 6}$}
\rput(-6.6,6.35){${\scriptscriptstyle 7}$}
% Path 4:
\rput(-9.6,4.35){${\scriptscriptstyle 5}$}
\rput(-8.6,6.35){${\scriptscriptstyle 7}$}
% Path 5:
\rput(-11.6,2.35){${\scriptscriptstyle 3}$}
% Path 6:
\rput(-12.6,3.35){${\scriptscriptstyle 4}$}
% Path 7:
\rput(-13.6,4.35){${\scriptscriptstyle 5}$}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-5.1,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-7.1,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-8.1,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-10.1,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-12.1,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-13.1,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-14.1,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-1.1,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-5.1,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-6.1,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-8.1,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-11.1,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-12.1,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](-13.1,7.1){0.3}
% The lattice paths corresponding to T2
% Lattice paths:
% Path 1:
\psline[linewidth=0.15,linecolor=black](-5.9,-0.1)(-5.9,4.9)(-4.9,4.9)(-3.9,4.9)(-3.9,6.9)(-2.9,6.9)(-1.9,6.9)
% Path 2:
\psline[linewidth=0.15,linecolor=black](-7.9,-0.1)(-7.9,3.9)(-6.9,3.9)(-6.9,5.9)(-5.9,5.9)(-5.9,6.9)
% Path 3:
\psline[linewidth=0.15,linecolor=black](-8.9,-0.1)(-8.9,4.9)(-7.9,4.9)(-7.9,6.9)(-6.9,6.9)
% Path 4:
\psline[linewidth=0.15,linecolor=black](-10.9,-0.1)(-10.9,2.9)(-9.9,2.9)(-9.9,5.9)(-8.9,5.9)(-8.9,6.9)
% Path 5:
\psline[linewidth=0.15,linecolor=black](-12.9,-0.1)(-12.9,1.9)(-11.9,1.9)(-11.9,6.9)
% Path 6:
\psline[linewidth=0.15,linecolor=black](-13.9,-0.1)(-13.9,5.9)(-12.9,5.9)(-12.9,6.9)
% Path 7:
\psline[linewidth=0.15,linecolor=black](-14.9,-0.1)(-14.9,6.9)(-13.9,6.9)
% Lattice path labels:
% Path 1:
\rput(-5.4,4.65){${\scriptscriptstyle 6}$}
\rput(-4.4,4.65){${\scriptscriptstyle 6}$}
\rput(-3.4,6.65){${\scriptscriptstyle 8}$}
\rput(-2.4,6.65){${\scriptscriptstyle 8}$}
% Path 2:
\rput(-7.4,3.65){${\scriptscriptstyle 5}$}
\rput(-6.4,5.65){${\scriptscriptstyle 7}$}
% Path 3:
\rput(-8.4,4.65){${\scriptscriptstyle 6}$}
\rput(-7.4,6.65){${\scriptscriptstyle 8}$}
% Path 4:
\rput(-10.4,2.65){${\scriptscriptstyle 4}$}
\rput(-9.4,5.65){${\scriptscriptstyle 7}$}
% Path 5:
\rput(-12.4,1.65){${\scriptscriptstyle 3}$}
% Path 6:
\rput(-13.4,5.65){${\scriptscriptstyle 7}$}
% Path 7:
\rput(-14.4,6.65){${\scriptscriptstyle 8}$}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-5.9,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-7.9,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-8.9,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-10.9,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-12.9,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-13.9,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-14.9,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-1.9,6.9){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-5.9,6.9){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-6.9,6.9){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-8.9,6.9){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-11.9,6.9){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-12.9,6.9){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](-13.9,6.9){0.3}
% The Young tableaux
% The grid for the skew Ferrers diagram:
% The horizontal lines:
\psline[linewidth=0.085,linecolor=gray](3.55556,-2)(5.88889,-2)
\psline[linewidth=0.085,linecolor=gray](3.55556,-2.77778)(5.88889,-2.77778)
\psline[linewidth=0.085,linecolor=gray](2.77778,-3.55556)(4.33333,-3.55556)
\psline[linewidth=0.085,linecolor=gray](2.77778,-4.33333)(4.33333,-4.33333)
\psline[linewidth=0.085,linecolor=gray](2.77778,-5.11111)(3.55556,-5.11111)
\psline[linewidth=0.085,linecolor=gray](2.77778,-5.88889)(3.55556,-5.88889)
\psline[linewidth=0.085,linecolor=gray](2,-6.66667)(2.77778,-6.66667)
\psline[linewidth=0.085,linecolor=gray](2,-7.44444)(2.77778,-7.44444)
\psline[linewidth=0.085,linecolor=gray](2,-8.22222)(2.77778,-8.22222)
% The vertical lines:
\psline[linewidth=0.085,linecolor=gray](2,-5.88889)(2,-8.22222)
\psline[linewidth=0.085,linecolor=gray](2.77778,-5.88889)(2.77778,-8.22222)
\psline[linewidth=0.085,linecolor=gray](3.55556,-2.77778)(3.55556,-5.88889)
\psline[linewidth=0.085,linecolor=gray](4.33333,-2)(4.33333,-4.33333)
\psline[linewidth=0.085,linecolor=gray](5.11111,-2)(5.11111,-2.77778)
\psline[linewidth=0.085,linecolor=gray](5.88889,-2)(5.88889,-2.77778)
\pspolygon[linewidth=0.2,linecolor=gray](5.88889,-2)(5.88889,-2.77778)(4.33333,-2.77778)(4.33333,-4.33333)(3.55556,-4.33333)(3.55556,-5.88889)(2.77778,-5.88889)(2.77778,-8.22222)(2,-8.22222)(2,-5.88889)(2.77778,-5.88889)(2.77778,-2.77778)(3.55556,-2.77778)(3.55556,-2)
% Young tableau labels:
% Row 1:
\rput(3.94444,-2.38889){${\scriptstyle\mathbf 1}$}
\rput(4.72222,-2.38889){${\scriptstyle\mathbf 8}$}
\rput(5.5,-2.38889){${\scriptstyle\mathbf 8}$}
% Row 2:
\rput(3.16667,-3.16667){${\scriptstyle\mathbf 3}$}
\rput(3.94444,-3.16667){${\scriptstyle\mathbf 3}$}
% Row 3:
\rput(3.16667,-3.94444){${\scriptstyle\mathbf 5}$}
\rput(3.94444,-3.94444){${\scriptstyle\mathbf 7}$}
% Row 4:
\rput(3.16667,-4.72222){${\scriptstyle\mathbf 6}$}
% Row 5:
\rput(3.16667,-5.5){${\scriptstyle\mathbf 7}$}
% Row 6:
\rput(2.38889,-6.27778){${\scriptstyle\mathbf 3}$}
% Row 7:
\rput(2.38889,-7.05556){${\scriptstyle\mathbf 4}$}
% Row 8:
\rput(2.38889,-7.83333){${\scriptstyle\mathbf 5}$}
% The grid for the skew Ferrers diagram:
% The horizontal lines:
\psline[linewidth=0.085,linecolor=gray](10.1111,-2)(14.,-2)
\psline[linewidth=0.085,linecolor=gray](10.1111,-2.77778)(14.,-2.77778)
\psline[linewidth=0.085,linecolor=gray](9.33333,-3.55556)(10.8889,-3.55556)
\psline[linewidth=0.085,linecolor=gray](7.77778,-4.33333)(10.8889,-4.33333)
\psline[linewidth=0.085,linecolor=gray](7,-5.11111)(7.77778,-5.11111)
\psline[linewidth=0.085,linecolor=gray](7,-5.88889)(7.77778,-5.88889)
\psline[linewidth=0.085,linecolor=gray](7,-6.66667)(7.77778,-6.66667)
% The vertical lines:
\psline[linewidth=0.085,linecolor=gray](7,-4.33333)(7,-6.66667)
\psline[linewidth=0.085,linecolor=gray](7.77778,-4.33333)(7.77778,-6.66667)
\psline[linewidth=0.085,linecolor=gray](8.55556,-3.55556)(8.55556,-4.33333)
\psline[linewidth=0.085,linecolor=gray](9.33333,-3.55556)(9.33333,-4.33333)
\psline[linewidth=0.085,linecolor=gray](10.1111,-2.77778)(10.1111,-4.33333)
\psline[linewidth=0.085,linecolor=gray](10.8889,-2)(10.8889,-4.33333)
\psline[linewidth=0.085,linecolor=gray](11.6667,-2)(11.6667,-2.77778)
\psline[linewidth=0.085,linecolor=gray](12.4444,-2)(12.4444,-2.77778)
\psline[linewidth=0.085,linecolor=gray](13.2222,-2)(13.2222,-2.77778)
\psline[linewidth=0.085,linecolor=gray](14.,-2)(14.,-2.77778)
\pspolygon[linewidth=0.2,linecolor=black](14.,-2)(14.,-2.77778)(10.8889,-2.77778)(10.8889,-4.33333)(7.77778,-4.33333)(7.77778,-6.66667)(7,-6.66667)(7,-4.33333)(7.77778,-4.33333)(7.77778,-3.55556)(9.33333,-3.55556)(9.33333,-2.77778)(10.1111,-2.77778)(10.1111,-2)
% Young tableau labels:
% Row 1:
\rput(10.5,-2.38889){${\scriptstyle\mathbf 6}$}
\rput(11.2778,-2.38889){${\scriptstyle\mathbf 6}$}
\rput(12.0556,-2.38889){${\scriptstyle\mathbf 6}$}
\rput(12.8333,-2.38889){${\scriptstyle\mathbf 6}$}
\rput(13.6111,-2.38889){${\scriptstyle\mathbf 7}$}
% Row 2:
\rput(9.72222,-3.16667){${\scriptstyle\mathbf 6}$}
\rput(10.5,-3.16667){${\scriptstyle\mathbf 7}$}
% Row 3:
\rput(8.16667,-3.94444){${\scriptstyle\mathbf 4}$}
\rput(8.94444,-3.94444){${\scriptstyle\mathbf 5}$}
\rput(9.72222,-3.94444){${\scriptstyle\mathbf 7}$}
\rput(10.5,-3.94444){${\scriptstyle\mathbf 8}$}
% Row 4:
\rput(7.38889,-4.72222){${\scriptstyle\mathbf 3}$}
% Row 5:
\rput(7.38889,-5.5){${\scriptstyle\mathbf 7}$}
% Row 6:
\rput(7.38889,-6.27778){${\scriptstyle\mathbf 8}$}
% The square grid with labels
% Square grid:
% The vertical lines:
\psline[linewidth=0.085,linecolor=lightgray](1,0)(1,7)
\psline[linewidth=0.085,linecolor=lightgray](2,0)(2,7)
\psline[linewidth=0.085,linecolor=lightgray](3,0)(3,7)
\psline[linewidth=0.085,linecolor=lightgray](4,0)(4,7)
\psline[linewidth=0.085,linecolor=lightgray](5,0)(5,7)
\psline[linewidth=0.085,linecolor=lightgray](6,0)(6,7)
\psline[linewidth=0.085,linecolor=lightgray](7,0)(7,7)
\psline[linewidth=0.085,linecolor=lightgray](8,0)(8,7)
\psline[linewidth=0.085,linecolor=lightgray](9,0)(9,7)
\psline[linewidth=0.085,linecolor=lightgray](10,0)(10,7)
\psline[linewidth=0.085,linecolor=lightgray](11,0)(11,7)
\psline[linewidth=0.085,linecolor=lightgray](12,0)(12,7)
\psline[linewidth=0.085,linecolor=lightgray](13,0)(13,7)
\psline[linewidth=0.085,linecolor=lightgray](14,0)(14,7)
\psline[linewidth=0.085,linecolor=lightgray](15,0)(15,7)
% The horizontal lines:
\psline[linewidth=0.085,linecolor=lightgray](1,0)(15,0)
\psline[linewidth=0.085,linecolor=lightgray](1,1)(15,1)
\psline[linewidth=0.085,linecolor=lightgray](1,2)(15,2)
\psline[linewidth=0.085,linecolor=lightgray](1,3)(15,3)
\psline[linewidth=0.085,linecolor=lightgray](1,4)(15,4)
\psline[linewidth=0.085,linecolor=lightgray](1,5)(15,5)
\psline[linewidth=0.085,linecolor=lightgray](1,6)(15,6)
\psline[linewidth=0.085,linecolor=lightgray](1,7)(15,7)
% Ray of labels:
\rput(1,-1){${\scriptscriptstyle -7}$}
\rput(2,-1){${\scriptscriptstyle -6}$}
\rput(3,-1){${\scriptscriptstyle -5}$}
\rput(4,-1){${\scriptscriptstyle -4}$}
\rput(5,-1){${\scriptscriptstyle -3}$}
\rput(6,-1){${\scriptscriptstyle -2}$}
\rput(7,-1){${\scriptscriptstyle -1}$}
\rput(8,-1){${\scriptscriptstyle 0}$}
\rput(9,-1){${\scriptscriptstyle 1}$}
\rput(10,-1){${\scriptscriptstyle 2}$}
\rput(11,-1){${\scriptscriptstyle 3}$}
\rput(12,-1){${\scriptscriptstyle 4}$}
\rput(13,-1){${\scriptscriptstyle 5}$}
\rput(14,-1){${\scriptscriptstyle 6}$}
\rput(15,-1){${\scriptscriptstyle 7}$}
% The recolouring paths
\psline[linecolor=gray,linewidth=0.3,linearc=0.6](15,7)(15,6)(14,6)(14,5)(12,5)(12,7)(14,7)
\psline[linecolor=gray,linewidth=0.3,linearc=0.6](7,7)(7,6)(8,6)(8,5)(9,5)(9,4)(8,4)(8,5)(7,5)(7,6)(6,6)(6,4)(7,4)(7,0)
% The lattice paths corresponding to T3
% Lattice paths:
% Path 1:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](10.9,0.1)(11.9,0.1)(11.9,7.1)(12.9,7.1)(13.9,7.1)
% Path 2:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](8.9,0.1)(8.9,2.1)(9.9,2.1)(10.9,2.1)(10.9,7.1)
% Path 3:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](7.9,0.1)(7.9,4.1)(8.9,4.1)(8.9,6.1)(9.9,6.1)(9.9,7.1)
% Path 4:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](6.9,0.1)(6.9,5.1)(7.9,5.1)(7.9,7.1)
% Path 5:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](5.9,0.1)(5.9,6.1)(6.9,6.1)(6.9,7.1)
% Path 6:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](3.9,0.1)(3.9,2.1)(4.9,2.1)(4.9,7.1)
% Path 7:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](2.9,0.1)(2.9,3.1)(3.9,3.1)(3.9,7.1)
% Path 8:
\psline[linewidth=0.15,linecolor=black,linestyle=dashed,dash=3pt 2pt](1.9,0.1)(1.9,4.1)(2.9,4.1)(2.9,7.1)
% Lattice path labels:
% Path 1:
\rput(11.4,0.35){${\scriptscriptstyle 1}$}
\rput(12.4,7.35){${\scriptscriptstyle 8}$}
\rput(13.4,7.35){${\scriptscriptstyle 8}$}
% Path 2:
\rput(9.4,2.35){${\scriptscriptstyle 3}$}
\rput(10.4,2.35){${\scriptscriptstyle 3}$}
% Path 3:
\rput(8.4,4.35){${\scriptscriptstyle 5}$}
\rput(9.4,6.35){${\scriptscriptstyle 7}$}
% Path 4:
\rput(7.4,5.35){${\scriptscriptstyle 6}$}
% Path 5:
\rput(6.4,6.35){${\scriptscriptstyle 7}$}
% Path 6:
\rput(4.4,2.35){${\scriptscriptstyle 3}$}
% Path 7:
\rput(3.4,3.35){${\scriptscriptstyle 4}$}
% Path 8:
\rput(2.4,4.35){${\scriptscriptstyle 5}$}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](10.9,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](8.9,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](7.9,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](6.9,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](5.9,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](3.9,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](2.9,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](1.9,0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](13.9,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](10.9,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](9.9,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](7.9,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](6.9,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](4.9,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](3.9,7.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white](2.9,7.1){0.3}
% The lattice paths corresponding to T$
% Lattice paths:
% Path 1:
\psline[linewidth=0.15,linecolor=black](10.1,-0.1)(10.1,4.9)(11.1,4.9)(12.1,4.9)(13.1,4.9)(14.1,4.9)(14.1,5.9)(15.1,5.9)(15.1,6.9)
% Path 2:
\psline[linewidth=0.15,linecolor=black](8.1,-0.1)(8.1,4.9)(9.1,4.9)(9.1,5.9)(10.1,5.9)(10.1,6.9)
% Path 3:
\psline[linewidth=0.15,linecolor=black](5.1,-0.1)(5.1,2.9)(6.1,2.9)(6.1,3.9)(7.1,3.9)(7.1,5.9)(8.1,5.9)(8.1,6.9)(9.1,6.9)
% Path 4:
\psline[linewidth=0.15,linecolor=black](3.1,-0.1)(3.1,1.9)(4.1,1.9)(4.1,6.9)
% Path 5:
\psline[linewidth=0.15,linecolor=black](2.1,-0.1)(2.1,5.9)(3.1,5.9)(3.1,6.9)
% Path 6:
\psline[linewidth=0.15,linecolor=black](1.1,-0.1)(1.1,6.9)(2.1,6.9)
% Lattice path labels:
% Path 1:
\rput(10.6,4.65){${\scriptscriptstyle 6}$}
\rput(11.6,4.65){${\scriptscriptstyle 6}$}
\rput(12.6,4.65){${\scriptscriptstyle 6}$}
\rput(13.6,4.65){${\scriptscriptstyle 6}$}
\rput(14.6,5.65){${\scriptscriptstyle 7}$}
% Path 2:
\rput(8.6,4.65){${\scriptscriptstyle 6}$}
\rput(9.6,5.65){${\scriptscriptstyle 7}$}
% Path 3:
\rput(5.6,2.65){${\scriptscriptstyle 4}$}
\rput(6.6,3.65){${\scriptscriptstyle 5}$}
\rput(7.6,5.65){${\scriptscriptstyle 7}$}
\rput(8.6,6.65){${\scriptscriptstyle 8}$}
% Path 4:
\rput(3.6,1.65){${\scriptscriptstyle 3}$}
% Path 5:
\rput(2.6,5.65){${\scriptscriptstyle 7}$}
% Path 6:
\rput(1.6,6.65){${\scriptscriptstyle 8}$}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](10.1,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](8.1,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](5.1,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](3.1,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](2.1,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](1.1,-0.1){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](15.1,6.9){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](10.1,6.9){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](9.1,6.9){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](4.1,6.9){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](3.1,6.9){0.3}
\pscircle[linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=black](2.1,6.9){0.3}
%
\endpspicture