
The Cayley Table for Z_7

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

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).

016****
056****
03**4**
03**6**
01****2
05****6
0*2*5**
0*3*5**
0*2**4*
0*3**5*
0**14**
0**36**
0**2*4*
0**2*5*
0**1**4
0**3**4
0****12
0****16

Number of incompletable partial transversals including (0,0,0): 18


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**** --- 0123456 --- 0246135
013**** --- 0135264 --- 0251643
014**** --- 0142635 --- 0265314
023**** --- 0236415 --- 0352164
024**** --- 0246135 --- 0362514
026**** --- 0263145 --- 0316524
031**** --- 0315246 --- 0431625
034**** --- 0346152 --- 0462531
036**** --- 0362514 --- 0415263
041**** --- 0416235 --- 0532614
042**** --- 0425613 --- 0541362
046**** --- 0461253 --- 0514632
051**** --- 0512463 --- 0635142
052**** --- 0526134 --- 0642513
053**** --- 0531642 --- 0654321
01*2*** --- 0142635 --- 0265314
01*3*** --- 0123456 --- 0246135
01*5*** --- 0135264 --- 0251643
02*1*** --- 0241536 --- 0364215
02*3*** --- 0263145 --- 0316524
02*5*** --- 0245163 --- 0361542
02*6*** --- 0246135 --- 0362514
03*2*** --- 0362514 --- 0415263
03*5*** --- 0315246 --- 0431625
03*6*** --- 0346152 --- 0462531
04*1*** --- 0461253 --- 0514632
04*3*** --- 0413562 --- 0536241
04*5*** --- 0425613 --- 0541362
04*6*** --- 0416235 --- 0532614
05*1*** --- 0531642 --- 0654321
05*2*** --- 0512463 --- 0635142
05*6*** --- 0526134 --- 0642513
01**2** --- 0135264 --- 0251643
01**4** --- 0123456 --- 0246135
01**6** --- 0142635 --- 0265314
02**1** --- 0263145 --- 0316524
02**4** --- 0236415 --- 0352164
02**5** --- 0241536 --- 0364215
03**1** --- 0346152 --- 0462531
03**2** --- 0315246 --- 0431625
03**5** --- 0362514 --- 0415263
04**2** --- 0461253 --- 0514632
04**5** --- 0413562 --- 0536241
04**6** --- 0425613 --- 0541362
05**1** --- 0526134 --- 0642513
05**4** --- 0512463 --- 0635142
05**6** --- 0531642 --- 0654321
01***3* --- 0142635 --- 0265314
01***5* --- 0123456 --- 0246135
01***6* --- 0135264 --- 0251643
02***1* --- 0236415 --- 0352164
02***3* --- 0246135 --- 0362514
02***4* --- 0263145 --- 0316524
02***6* --- 0245163 --- 0361542
03***1* --- 0362514 --- 0415263
03***4* --- 0315246 --- 0431625
03***5* --- 0346152 --- 0462531
04***1* --- 0425613 --- 0541362
04***3* --- 0416235 --- 0532614
04***5* --- 0461253 --- 0514632
04***6* --- 0415263 --- 0531642
05***3* --- 0526134 --- 0642513
05***4* --- 0531642 --- 0654321
05***6* --- 0512463 --- 0635142
01****4 --- 0135264 --- 0251643
01****5 --- 0142635 --- 0265314
01****6 --- 0123456 --- 0246135
02****3 --- 0245163 --- 0361542
02****5 --- 0263145 --- 0316524
02****6 --- 0241536 --- 0364215
03****2 --- 0346152 --- 0462531
03****4 --- 0362514 --- 0415263
03****6 --- 0315246 --- 0431625
04****2 --- 0413562 --- 0536241
04****3 --- 0461253 --- 0514632
04****5 --- 0416235 --- 0532614
05****2 --- 0531642 --- 0654321
05****3 --- 0512463 --- 0635142
05****4 --- 0526134 --- 0642513
0*12*** --- 0512463 --- 0635142
0*13*** --- 0413562 --- 0536241
0*15*** --- 0415263 --- 0531642
0*16*** --- 0416235 --- 0532614
0*23*** --- 0123456 --- 0246135
0*25*** --- 0425613 --- 0541362
0*26*** --- 0526134 --- 0642513
0*31*** --- 0531642 --- 0654321
0*35*** --- 0135264 --- 0251643
0*36*** --- 0236415 --- 0352164
0*41*** --- 0241536 --- 0364215
0*42*** --- 0142635 --- 0265314
0*45*** --- 0245163 --- 0361542
0*46*** --- 0346152 --- 0462531
0*61*** --- 0461253 --- 0514632
0*62*** --- 0362514 --- 0415263
0*63*** --- 0263145 --- 0316524
0*1*2** --- 0416235 --- 0532614
0*1*4** --- 0512463 --- 0635142
0*1*5** --- 0413562 --- 0536241
0*2*1** --- 0526134 --- 0642513
0*2*4** --- 0123456 --- 0246135
0*2*6** --- 0425613 --- 0541362
0*3*2** --- 0135264 --- 0251643
0*3*4** --- 0236415 --- 0352164
0*3*6** --- 0531642 --- 0654321
0*4*1** --- 0346152 --- 0462531
0*4*5** --- 0241536 --- 0364215
0*4*6** --- 0142635 --- 0265314
0*6*1** --- 0263145 --- 0316524
0*6*2** --- 0461253 --- 0514632
0*6*5** --- 0362514 --- 0415263
0*1**3* --- 0416235 --- 0532614
0*1**4* --- 0315246 --- 0431625
0*1**6* --- 0512463 --- 0635142
0*2**1* --- 0425613 --- 0541362
0*2**3* --- 0526134 --- 0642513
0*2**5* --- 0123456 --- 0246135
0*3**1* --- 0236415 --- 0352164
0*3**4* --- 0531642 --- 0654321
0*3**6* --- 0135264 --- 0251643
0*4**3* --- 0246135 --- 0362514
0*4**5* --- 0346152 --- 0462531
0*4**6* --- 0245163 --- 0361542
0*6**1* --- 0362514 --- 0415263
0*6**4* --- 0263145 --- 0316524
0*6**5* --- 0461253 --- 0514632
0*1***2 --- 0413562 --- 0536241
0*1***3 --- 0512463 --- 0635142
0*1***5 --- 0416235 --- 0532614
0*1***6 --- 0315246 --- 0431625
0*2***3 --- 0425613 --- 0541362
0*2***4 --- 0526134 --- 0642513
0*2***6 --- 0123456 --- 0246135
0*3***2 --- 0531642 --- 0654321
0*3***4 --- 0135264 --- 0251643
0*3***5 --- 0236415 --- 0352164
0*4***2 --- 0346152 --- 0462531
0*4***3 --- 0245163 --- 0361542
0*4***5 --- 0246135 --- 0362514
0*4***6 --- 0241536 --- 0364215
0*6***3 --- 0461253 --- 0514632
0*6***4 --- 0362514 --- 0415263
0*6***5 --- 0263145 --- 0316524
0**12** --- 0461253 --- 0514632
0**15** --- 0241536 --- 0364215
0**16** --- 0531642 --- 0654321
0**24** --- 0512463 --- 0635142
0**25** --- 0362514 --- 0415263
0**26** --- 0142635 --- 0265314
0**31** --- 0263145 --- 0316524
0**34** --- 0123456 --- 0246135
0**35** --- 0413562 --- 0536241
0**51** --- 0245163 --- 0361542
0**52** --- 0415263 --- 0531642
0**56** --- 0425613 --- 0541362
0**61** --- 0526134 --- 0642513
0**62** --- 0416235 --- 0532614
0**64** --- 0236415 --- 0352164
0**1*3* --- 0241536 --- 0364215
0**1*4* --- 0531642 --- 0654321
0**1*5* --- 0461253 --- 0514632
0**2*1* --- 0362514 --- 0415263
0**2*3* --- 0142635 --- 0265314
0**2*6* --- 0512463 --- 0635142
0**3*4* --- 0263145 --- 0316524
0**3*5* --- 0123456 --- 0246135
0**3*6* --- 0413562 --- 0536241
0**5*1* --- 0425613 --- 0541362
0**5*4* --- 0315246 --- 0431625
0**5*6* --- 0415263 --- 0531642
0**6*1* --- 0236415 --- 0352164
0**6*3* --- 0526134 --- 0642513
0**6*5* --- 0346152 --- 0462531
0**1**2 --- 0531642 --- 0654321
0**1**3 --- 0461253 --- 0514632
0**1**6 --- 0241536 --- 0364215
0**2**3 --- 0512463 --- 0635142
0**2**4 --- 0362514 --- 0415263
0**2**5 --- 0142635 --- 0265314
0**3**2 --- 0413562 --- 0536241
0**3**5 --- 0263145 --- 0316524
0**3**6 --- 0123456 --- 0246135
0**5**3 --- 0425613 --- 0541362
0**5**4 --- 0135264 --- 0251643
0**5**6 --- 0315246 --- 0431625
0**6**2 --- 0346152 --- 0462531
0**6**4 --- 0526134 --- 0642513
0**6**5 --- 0416235 --- 0532614
0***13* --- 0526134 --- 0642513
0***14* --- 0263145 --- 0316524
0***15* --- 0346152 --- 0462531
0***16* --- 0245163 --- 0361542
0***23* --- 0416235 --- 0532614
0***24* --- 0315246 --- 0431625
0***25* --- 0461253 --- 0514632
0***26* --- 0415263 --- 0531642
0***41* --- 0236415 --- 0352164
0***45* --- 0123456 --- 0246135
0***46* --- 0512463 --- 0635142
0***51* --- 0362514 --- 0415263
0***53* --- 0241536 --- 0364215
0***56* --- 0413562 --- 0536241
0***61* --- 0425613 --- 0541362
0***63* --- 0142635 --- 0265314
0***64* --- 0531642 --- 0654321
0***1*2 --- 0346152 --- 0462531
0***1*3 --- 0245163 --- 0361542
0***1*4 --- 0526134 --- 0642513
0***1*5 --- 0263145 --- 0316524
0***2*3 --- 0461253 --- 0514632
0***2*4 --- 0135264 --- 0251643
0***2*5 --- 0416235 --- 0532614
0***2*6 --- 0315246 --- 0431625
0***4*3 --- 0512463 --- 0635142
0***4*5 --- 0236415 --- 0352164
0***4*6 --- 0123456 --- 0246135
0***5*2 --- 0413562 --- 0536241
0***5*4 --- 0362514 --- 0415263
0***5*6 --- 0241536 --- 0364215
0***6*2 --- 0531642 --- 0654321
0***6*3 --- 0425613 --- 0541362
0***6*5 --- 0142635 --- 0265314
0****13 --- 0425613 --- 0541362
0****14 --- 0362514 --- 0415263
0****15 --- 0236415 --- 0352164
0****34 --- 0526134 --- 0642513
0****35 --- 0416235 --- 0532614
0****36 --- 0241536 --- 0364215
0****42 --- 0531642 --- 0654321
0****45 --- 0263145 --- 0316524
0****46 --- 0315246 --- 0431625
0****52 --- 0346152 --- 0462531
0****53 --- 0461253 --- 0514632
0****56 --- 0123456 --- 0246135
0****62 --- 0413562 --- 0536241
0****63 --- 0512463 --- 0635142
0****64 --- 0135264 --- 0251643

