A Rational Catalan Formula for $(m,3)$-Hikita Polynomials
Keywords: Catalan, Dyck path, Parking function, Shuffle theorem, Rational shuffle theorem
AbstractHikita polynomials are the combinatorial side of the rational shuffle theorem. Building upon a recent formula for $(m,3)$-Catalan polynomials, we prove a formula for $(m,3)$-Hikita polynomials in terms of Catalan polynomials. This formula shows a surprising relation among coefficients of Hikita polynomials and implies deeper recursive relations and proves the $q,t$-symmetry of $(m,3)$-Hikita polynomials.