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Minimum number of diagonal transversals in a semicyclic diagonal Latin square of order 2n+1.
2

%I #15 Nov 24 2023 17:54:22

%S 1,0,5,27,0,4523,127339,0,204330233,11232045257,0

%N Minimum number of diagonal transversals in a semicyclic diagonal Latin square of order 2n+1.

%C A horizontally semicyclic diagonal Latin square is a square where each row r(i) is a cyclic shift of the first row r(0) by some value d(i) (see example). Similarly, a vertically semicyclic diagonal Latin square is a square where each column c(i) is a cyclic shift of the first column c(0) by some value d(i).

%H Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2443">About the spectra of numerical characteristics of different types of cyclic diagonal Latin squsres</a> (in Russian).

%H Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2450">About the spectra of numerical characteristics of semicyclic diagonal Latin squares of order 17</a> (in Russian).

%H Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2453">About the spectra of numerical characteristics of semicyclic diagonal Latin squares of order 19</a> (in Russian).

%H Eduard I. Vatutin, <a href="/A366332/a366332.txt">Proving list (best known examples)</a>.

%H <a href="https://oeis.org/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.

%e Example of horizontally semicyclic diagonal Latin square of order 13:

%e 0 1 2 3 4 5 6 7 8 9 10 11 12

%e 2 3 4 5 6 7 8 9 10 11 12 0 1 (d=2)

%e 4 5 6 7 8 9 10 11 12 0 1 2 3 (d=4)

%e 9 10 11 12 0 1 2 3 4 5 6 7 8 (d=9)

%e 7 8 9 10 11 12 0 1 2 3 4 5 6 (d=7)

%e 12 0 1 2 3 4 5 6 7 8 9 10 11 (d=12)

%e 3 4 5 6 7 8 9 10 11 12 0 1 2 (d=3)

%e 11 12 0 1 2 3 4 5 6 7 8 9 10 (d=11)

%e 6 7 8 9 10 11 12 0 1 2 3 4 5 (d=6)

%e 1 2 3 4 5 6 7 8 9 10 11 12 0 (d=1)

%e 5 6 7 8 9 10 11 12 0 1 2 3 4 (d=5)

%e 10 11 12 0 1 2 3 4 5 6 7 8 9 (d=10)

%e 8 9 10 11 12 0 1 2 3 4 5 6 7 (d=8)

%Y Cf. A071607, A342990, A342997, A342998, A348212, A366331.

%K nonn,more,hard

%O 0,3

%A _Eduard I. Vatutin_, Oct 07 2023