
The Cayley Table for Z_9

       0  1  2  3  4  5  6  7  8
    ----------------------------
  0 |  0  1  2  3  4  5  6  7  8
  1 |  1  2  3  4  5  6  7  8  0
  2 |  2  3  4  5  6  7  8  0  1
  3 |  3  4  5  6  7  8  0  1  2
  4 |  4  5  6  7  8  0  1  2  3
  5 |  5  6  7  8  0  1  2  3  4
  6 |  6  7  8  0  1  2  3  4  5
  7 |  7  8  0  1  2  3  4  5  6
  8 |  8  0  1  2  3  4  5  6  7

Incompletable partial transversals
----------------------------------

Each partial transversal of length 3 which is incompletable is given below.
For example, 0*2***8** corresponds to the partial transversal with cells
at (0,0), (2,2), and (6,8).


Number of incompletable partial transversals including (0,0,0): 0


Completions of completable partial transversals
-----------------------------------------------

Each partial transversal of length 3 which is completable is given below.
For example, 0*2***8** corresponds to the partial transversal with cells
at (0,0), (2,2), and (6,8).

After each partial transversal should be two permutations. The first
correponds to the cell locations for a completion of the partial transversal.
The second contains the symbols in each cell of the completion.

012****** --- 012537486 --- 024873165
013****** --- 013742685 --- 025187364
014****** --- 014738256 --- 026174835
015****** --- 015723864 --- 027168543
016****** --- 016427835 --- 028763514
018****** --- 018423756 --- 021768435
023****** --- 023845167 --- 035281746
024****** --- 024863175 --- 036218754
025****** --- 025841736 --- 037286415
026****** --- 026831475 --- 038276154
028****** --- 028531746 --- 031876425
031****** --- 031742586 --- 043187265
034****** --- 034782516 --- 046137285
035****** --- 035861274 --- 047216853
036****** --- 036825174 --- 048261753
038****** --- 038527146 --- 041863725
041****** --- 041835267 --- 053271846
042****** --- 042863157 --- 054218736
045****** --- 045781263 --- 057136842
046****** --- 046831752 --- 058276431
048****** --- 048527163 --- 051863742
051****** --- 051842736 --- 063287415
052****** --- 052863174 --- 064218753
053****** --- 053862714 --- 065217483
056****** --- 056812734 --- 068257413
058****** --- 058417263 --- 061753842
061****** --- 061823475 --- 073268154
062****** --- 062813457 --- 074258136
063****** --- 063841752 --- 075286431
064****** --- 064817235 --- 076253814
068****** --- 068317245 --- 071653824
071****** --- 071428536 --- 083764215
072****** --- 072831456 --- 084276135
073****** --- 073825164 --- 085261743
074****** --- 074812635 --- 086257314
075****** --- 075318642 --- 087654321
078****** --- 078312645 --- 081657324
01*2***** --- 016238457 --- 028574136
01*3***** --- 018342756 --- 021687435
01*4***** --- 018423756 --- 021768435
01*5***** --- 014582736 --- 026837415
01*7***** --- 015723864 --- 027168543
02*1***** --- 026135847 --- 038471526
02*3***** --- 028346175 --- 031682754
02*4***** --- 028413567 --- 031758246
02*5***** --- 028531746 --- 031876425
02*7***** --- 026731845 --- 038176524
02*8***** --- 026831475 --- 038276154
03*2***** --- 038246157 --- 041582736
03*4***** --- 038471256 --- 041726835
03*5***** --- 038527146 --- 041863725
03*7***** --- 036712584 --- 048157263
03*8***** --- 036825174 --- 048261753
04*1***** --- 048136257 --- 051472836
04*3***** --- 048372615 --- 051627384
04*5***** --- 048527163 --- 051863742
04*7***** --- 046728153 --- 058164732
04*8***** --- 046831752 --- 058276431
05*1***** --- 058142673 --- 061487352
05*2***** --- 058273164 --- 061528743
05*4***** --- 058417263 --- 061753842
05*7***** --- 052783146 --- 064138725
05*8***** --- 056812734 --- 068257413
06*1***** --- 068123574 --- 071468253
06*2***** --- 068241753 --- 071586432
06*3***** --- 068317245 --- 071653824
06*5***** --- 063581742 --- 075836421
06*7***** --- 064718253 --- 076154832
06*8***** --- 064817235 --- 076253814
07*1***** --- 075126834 --- 087462513
07*2***** --- 078231645 --- 081576324
07*3***** --- 078312645 --- 081657324
07*4***** --- 073481562 --- 085736241
07*8***** --- 074812635 --- 086257314
01**2**** --- 018423756 --- 021768435
01**3**** --- 016238457 --- 028574136
01**4**** --- 018342756 --- 021687435
01**6**** --- 015368274 --- 027614853
01**8**** --- 016382475 --- 028637154
02**1**** --- 028413567 --- 031758246
02**3**** --- 028531746 --- 031876425
02**4**** --- 028346175 --- 031682754
02**6**** --- 025163847 --- 037418526
02**7**** --- 026471835 --- 038726514
03**1**** --- 038512647 --- 041857326
03**2**** --- 038527146 --- 041863725
03**4**** --- 038246157 --- 041582736
03**6**** --- 035861274 --- 047216853
03**7**** --- 038471256 --- 041726835
03**8**** --- 036481572 --- 048736251
04**2**** --- 048527163 --- 051863742
04**3**** --- 048136257 --- 051472836
04**6**** --- 045167283 --- 057413862
04**7**** --- 048372615 --- 051627384
04**8**** --- 046182537 --- 058437216
05**1**** --- 058417263 --- 061753842
05**3**** --- 058236714 --- 061572483
05**4**** --- 058247163 --- 061583742
05**6**** --- 053862714 --- 065217483
05**7**** --- 058273164 --- 061528743
05**8**** --- 056182473 --- 068437152
06**1**** --- 068317245 --- 071653824
06**2**** --- 068123574 --- 071468253
06**4**** --- 068241753 --- 071586432
06**7**** --- 064173852 --- 076428531
06**8**** --- 064285713 --- 076531482
07**1**** --- 078312645 --- 081657324
07**2**** --- 075126834 --- 087462513
07**3**** --- 078231645 --- 081576324
07**6**** --- 074268153 --- 086514732
07**8**** --- 075281463 --- 087536142
01***2*** --- 018342756 --- 021687435
01***3*** --- 018423756 --- 021768435
01***5*** --- 016235784 --- 028571463
01***7*** --- 016427835 --- 028763514
01***8*** --- 016238457 --- 028574136
02***1*** --- 028531746 --- 031876425
02***3*** --- 028413567 --- 031758246
02***5*** --- 026415783 --- 038751462
02***6*** --- 028346175 --- 031682754
02***8*** --- 026418537 --- 038754216
03***1*** --- 038471256 --- 041726835
03***2*** --- 038512647 --- 041857326
03***5*** --- 036825174 --- 048261753
03***6*** --- 038526174 --- 041862753
03***7*** --- 038527146 --- 041863725
04***1*** --- 046831752 --- 058276431
04***2*** --- 048372615 --- 051627384
04***3*** --- 045173682 --- 057428361
04***5*** --- 042835617 --- 054271386
04***6*** --- 048136257 --- 051472836
04***7*** --- 048527163 --- 051863742
04***8*** --- 046728153 --- 058164732
05***2*** --- 058142673 --- 061487352
05***3*** --- 058273164 --- 061528743
05***6*** --- 058236714 --- 061572483
05***7*** --- 058417263 --- 061753842
05***8*** --- 056278134 --- 068524713
06***1*** --- 068241753 --- 071586432
06***3*** --- 068123574 --- 071468253
06***5*** --- 064285713 --- 076531482
06***7*** --- 068317245 --- 071653824
06***8*** --- 064718253 --- 076154832
07***1*** --- 078231645 --- 081576324
07***2*** --- 078312645 --- 081657324
07***5*** --- 074285163 --- 086531742
07***6*** --- 075126834 --- 087462513
07***8*** --- 075318642 --- 087654321
01****2** --- 015368274 --- 027614853
01****4** --- 016382475 --- 028637154
01****6** --- 018423675 --- 021768354
01****7** --- 018423756 --- 021768435
01****8** --- 016427835 --- 028763514
02****1** --- 028346175 --- 031682754
02****4** --- 026831475 --- 038276154
02****5** --- 028413567 --- 031758246
02****7** --- 028531746 --- 031876425
02****8** --- 026731845 --- 038176524
03****1** --- 038527146 --- 041863725
03****2** --- 038471256 --- 041726835
03****4** --- 036812457 --- 048257136
03****5** --- 038427516 --- 041763285
03****6** --- 038512647 --- 041857326
03****8** --- 036471852 --- 048726531
04****1** --- 048527163 --- 051863742
04****2** --- 048136257 --- 051472836
04****5** --- 046182537 --- 058437216
04****6** --- 048372615 --- 051627384
04****7** --- 046831752 --- 058276431
05****1** --- 058273164 --- 061528743
05****2** --- 058417263 --- 061753842
05****4** --- 056182473 --- 068437152
05****6** --- 058142673 --- 061487352
05****7** --- 058236714 --- 061572483
05****8** --- 056172834 --- 068427513
06****2** --- 068317245 --- 071653824
06****4** --- 063827415 --- 075263184
06****5** --- 068123574 --- 071468253
06****7** --- 068241753 --- 071586432
06****8** --- 064173852 --- 076428531
07****1** --- 074286135 --- 086532714
07****4** --- 075281463 --- 087536142
07****5** --- 078312564 --- 081657243
07****6** --- 078312645 --- 081657324
07****8** --- 075126834 --- 087462513
01*****3* --- 016427835 --- 028763514
01*****5* --- 018423756 --- 021768435
01*****6* --- 015723864 --- 027168543
01*****7* --- 018423675 --- 021768354
01*****8* --- 016237485 --- 028573164
02*****1* --- 025378416 --- 037624185
02*****3* --- 026471835 --- 038726514
02*****4* --- 028531746 --- 031876425
02*****6* --- 028413567 --- 031758246
02*****7* --- 028346175 --- 031682754
02*****8* --- 026415783 --- 038751462
03*****1* --- 038427516 --- 041763285
03*****4* --- 038527146 --- 041863725
03*****5* --- 038471256 --- 041726835
03*****7* --- 038526174 --- 041862753
03*****8* --- 036712584 --- 048157263
04*****1* --- 048372615 --- 051627384
04*****3* --- 046827135 --- 058263714
04*****5* --- 048136257 --- 051472836
04*****6* --- 048527163 --- 051863742
04*****8* --- 046137582 --- 058473261
05*****1* --- 058236714 --- 061572483
05*****3* --- 056812734 --- 068257413
05*****4* --- 058137246 --- 061473825
05*****6* --- 058417263 --- 061753842
05*****7* --- 058142673 --- 061487352
06*****1* --- 064285713 --- 076531482
06*****3* --- 064817235 --- 076253814
06*****4* --- 068317245 --- 071653824
06*****5* --- 068241753 --- 071586432
06*****7* --- 068123574 --- 071468253
06*****8* --- 063175284 --- 075421863
07*****3* --- 075126834 --- 087462513
07*****4* --- 078312645 --- 081657324
07*****5* --- 074268153 --- 086514732
07*****6* --- 078312564 --- 081657243
07*****8* --- 073162584 --- 085417263
01******2 --- 015348672 --- 027684351
01******4 --- 016235784 --- 028571463
01******5 --- 018423675 --- 021768354
01******6 --- 018423756 --- 021768435
01******7 --- 016238457 --- 028574136
01******8 --- 014263758 --- 026518437
02******3 --- 026415783 --- 038751462
02******5 --- 028346175 --- 031682754
02******6 --- 028531746 --- 031876425
02******7 --- 028413567 --- 031758246
02******8 --- 026315748 --- 038651427
03******2 --- 036481572 --- 048736251
03******4 --- 038526174 --- 041862753
03******6 --- 038527146 --- 041863725
03******7 --- 038512647 --- 041857326
03******8 --- 036271458 --- 048526137
04******2 --- 046831752 --- 058276431
04******3 --- 048527163 --- 051863742
04******5 --- 048372615 --- 051627384
04******7 --- 048136257 --- 051472836
04******8 --- 046127538 --- 058463217
05******2 --- 056137842 --- 068473521
05******3 --- 058417263 --- 061753842
05******4 --- 058273164 --- 061528743
05******6 --- 058137246 --- 061473825
05******8 --- 053167248 --- 065413827
06******2 --- 064813752 --- 076258431
06******3 --- 068241753 --- 071586432
06******4 --- 068123574 --- 071468253
06******5 --- 068317245 --- 071653824
06******7 --- 063185247 --- 075431826
07******2 --- 075318642 --- 087654321
07******3 --- 075281463 --- 087536142
07******4 --- 078312564 --- 081657243
07******5 --- 078312645 --- 081657324
07******6 --- 074182536 --- 086437215
07******8 --- 073126458 --- 085462137
0*12***** --- 071236485 --- 083572164
0*13***** --- 071362845 --- 083617524
0*14***** --- 071428536 --- 083764215
0*15***** --- 061528473 --- 073864152
0*17***** --- 061723845 --- 073168524
0*18***** --- 061823475 --- 073268154
0*23***** --- 072385146 --- 084631725
0*24***** --- 072481536 --- 084736215
0*25***** --- 062581473 --- 074836152
0*27***** --- 062741853 --- 074186532
0*28***** --- 072831456 --- 084276135
0*31***** --- 073162584 --- 085417263
0*34***** --- 073481562 --- 085736241
0*35***** --- 063581742 --- 075836421
0*37***** --- 063781245 --- 075136824
0*38***** --- 073825164 --- 085261743
0*41***** --- 074182536 --- 086437215
0*42***** --- 074286135 --- 086532714
0*45***** --- 034586172 --- 046832751
0*47***** --- 064718253 --- 076154832
0*48***** --- 074812635 --- 086257314
0*51***** --- 075126834 --- 087462513
0*52***** --- 075281463 --- 087536142
0*53***** --- 075318642 --- 087654321
0*57***** --- 045781263 --- 057136842
0*58***** --- 035861274 --- 047216853
0*61***** --- 056182473 --- 068437152
0*62***** --- 056278134 --- 068524713
0*63***** --- 046378152 --- 058624731
0*64***** --- 036481572 --- 048736251
0*67***** --- 046728153 --- 058164732
0*68***** --- 056812734 --- 068257413
0*81***** --- 068123574 --- 071468253
0*82***** --- 078231645 --- 081576324
0*83***** --- 078312645 --- 081657324
0*84***** --- 058417263 --- 061753842
0*85***** --- 048527163 --- 051863742
0*1*2**** --- 071428536 --- 083764215
0*1*3**** --- 071236485 --- 083572164
0*1*4**** --- 061348572 --- 073684251
0*1*6**** --- 071362845 --- 083617524
0*1*7**** --- 061273485 --- 073528164
0*2*1**** --- 072415683 --- 084751362
0*2*3**** --- 072831456 --- 084276135
0*2*4**** --- 062741853 --- 074186532
0*2*6**** --- 072461853 --- 084716532
0*2*7**** --- 062571834 --- 074826513
0*2*8**** --- 072481536 --- 084736215
0*3*2**** --- 073825164 --- 085261743
0*3*4**** --- 063841752 --- 075286431
0*3*6**** --- 073162584 --- 085417263
0*3*7**** --- 063175284 --- 075421863
0*3*8**** --- 073481562 --- 085736241
0*4*1**** --- 074812635 --- 086257314
0*4*3**** --- 074136852 --- 086472531
0*4*6**** --- 074268153 --- 086514732
0*4*7**** --- 064173852 --- 076428531
0*4*8**** --- 074286135 --- 086532714
0*5*1**** --- 075318642 --- 087654321
0*5*2**** --- 075126834 --- 087462513
0*5*4**** --- 035841672 --- 047286351
0*5*6**** --- 045167283 --- 057413862
0*5*7**** --- 045378612 --- 057624381
0*5*8**** --- 075281463 --- 087536142
0*6*1**** --- 056812734 --- 068257413
0*6*2**** --- 046827135 --- 058263714
0*6*3**** --- 056137842 --- 068473521
0*6*7**** --- 056278134 --- 068524713
0*6*8**** --- 056182473 --- 068437152
0*8*1**** --- 078312645 --- 081657324
0*8*2**** --- 068123574 --- 071468253
0*8*3**** --- 078231645 --- 081576324
0*8*4**** --- 068241753 --- 071586432
0*8*7**** --- 058273164 --- 061528743
0*1**2*** --- 071362845 --- 083617524
0*1**3*** --- 061823475 --- 073268154
0*1**5*** --- 071425863 --- 083761542
0*1**6*** --- 071426835 --- 083762514
0*1**8*** --- 071428536 --- 083764215
0*2**1*** --- 072831456 --- 084276135
0*2**3*** --- 062813457 --- 074258136
0*2**5*** --- 072415683 --- 084751362
0*2**6*** --- 072316458 --- 084652137
0*2**7*** --- 062517483 --- 074853162
0*3**1*** --- 073481562 --- 085736241
0*3**2*** --- 073162584 --- 085417263
0*3**5*** --- 073825164 --- 085261743
0*3**6*** --- 073126458 --- 085462137
0*3**7*** --- 063827415 --- 075263184
0*3**8*** --- 063728514 --- 075164283
0*4**2*** --- 074812635 --- 086257314
0*4**3*** --- 064813752 --- 076258431
0*4**5*** --- 074285163 --- 086531742
0*4**6*** --- 074286135 --- 086532714
0*4**7*** --- 064817235 --- 076253814
0*4**8*** --- 074268153 --- 086514732
0*5**1*** --- 075281463 --- 087536142
0*5**3*** --- 045173682 --- 057428361
0*5**6*** --- 075126834 --- 087462513
0*5**7*** --- 045167283 --- 057413862
0*5**8*** --- 075318642 --- 087654321
0*6**1*** --- 046831752 --- 058276431
0*6**2*** --- 056812734 --- 068257413
0*6**5*** --- 036825174 --- 048261753
0*6**7*** --- 056137842 --- 068473521
0*6**8*** --- 056278134 --- 068524713
0*8**1*** --- 078231645 --- 081576324
0*8**2*** --- 078312645 --- 081657324
0*8**3*** --- 068123574 --- 071468253
0*8**6*** --- 058236714 --- 061572483
0*8**7*** --- 068317245 --- 071653824
0*1***2** --- 051738246 --- 063174825
0*1***4** --- 071236485 --- 083572164
0*1***5** --- 071428536 --- 083764215
0*1***7** --- 061245783 --- 073581462
0*1***8** --- 071426835 --- 083762514
0*2***1** --- 072385146 --- 084631725
0*2***4** --- 072831456 --- 084276135
0*2***5** --- 072481536 --- 084736215
0*2***6** --- 072415683 --- 084751362
0*2***8** --- 072461853 --- 084716532
0*3***1** --- 073825164 --- 085261743
0*3***2** --- 063781245 --- 075136824
0*3***4** --- 073126458 --- 085462137
0*3***5** --- 073481562 --- 085736241
0*3***6** --- 073125648 --- 085461327
0*3***7** --- 063841752 --- 075286431
0*4***1** --- 074286135 --- 086532714
0*4***2** --- 064817235 --- 076253814
0*4***5** --- 074182536 --- 086437215
0*4***6** --- 074812635 --- 086257314
0*4***7** --- 064813752 --- 076258431
0*4***8** --- 074162853 --- 086417532
0*5***2** --- 045781263 --- 057136842
0*5***4** --- 075281463 --- 087536142
0*5***6** --- 075318642 --- 087654321
0*5***7** --- 045386712 --- 057632481
0*5***8** --- 075126834 --- 087462513
0*6***1** --- 056278134 --- 068524713
0*6***4** --- 056182473 --- 068437152
0*6***5** --- 046182537 --- 058437216
0*6***7** --- 056812734 --- 068257413
0*6***8** --- 056172834 --- 068427513
0*8***1** --- 058273164 --- 061528743
0*8***2** --- 068317245 --- 071653824
0*8***5** --- 078312564 --- 081657243
0*8***6** --- 078312645 --- 081657324
0*8***7** --- 068241753 --- 071586432
0*1****3* --- 071428536 --- 083764215
0*1****4* --- 071362845 --- 083617524
0*1****6* --- 071425863 --- 083761542
0*1****7* --- 061823475 --- 073268154
0*1****8* --- 071236485 --- 083572164
0*2****1* --- 062375814 --- 074621583
0*2****3* --- 072481536 --- 084736215
0*2****4* --- 072385146 --- 084631725
0*2****5* --- 072831456 --- 084276135
0*2****7* --- 062581473 --- 074836152
0*2****8* --- 072415683 --- 084751362
0*3****1* --- 063827415 --- 075263184
0*3****4* --- 073125648 --- 085461327
0*3****5* --- 073126458 --- 085462137
0*3****6* --- 073825164 --- 085261743
0*3****8* --- 073162584 --- 085417263
0*4****1* --- 064285713 --- 076531482
0*4****3* --- 074812635 --- 086257314
0*4****5* --- 074268153 --- 086514732
0*4****6* --- 074285163 --- 086531742
0*4****7* --- 064185273 --- 076431852
0*5****1* --- 045728613 --- 057164382
0*5****3* --- 075126834 --- 087462513
0*5****4* --- 075318642 --- 087654321
0*5****6* --- 075281463 --- 087536142
0*5****7* --- 035861274 --- 047216853
0*5****8* --- 045173682 --- 057428361
0*6****3* --- 056812734 --- 068257413
0*6****4* --- 056137842 --- 068473521
0*6****5* --- 046831752 --- 058276431
0*6****7* --- 056182473 --- 068437152
0*6****8* --- 046137582 --- 058473261
0*8****1* --- 058236714 --- 061572483
0*8****4* --- 078312645 --- 081657324
0*8****5* --- 068241753 --- 071586432
0*8****6* --- 078312564 --- 081657243
0*8****7* --- 068123574 --- 071468253
0*1*****2 --- 061348572 --- 073684251
0*1*****3 --- 071425863 --- 083761542
0*1*****5 --- 071426835 --- 083762514
0*1*****6 --- 071428536 --- 083764215
0*1*****7 --- 061248537 --- 073584216
0*1*****8 --- 051273468 --- 063528147
0*2*****3 --- 072461853 --- 084716532
0*2*****4 --- 062713584 --- 074158263
0*2*****6 --- 072831456 --- 084276135
0*2*****7 --- 062813457 --- 074258136
0*2*****8 --- 072316458 --- 084652137
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