|
A269516
|
|
Number of T(n) X T(n) matrices containing the multiset {1, 2, 2, 3, 3, 3, ..., n, n, ..., n} in each row and column, where T(n) = A000217(n).
|
|
0
|
|
|
%I #7 Aug 12 2022 20:17:55
%S 1,6,5450400
%N Number of T(n) X T(n) matrices containing the multiset {1, 2, 2, 3, 3, 3, ..., n, n, ..., n} in each row and column, where T(n) = A000217(n).
%C Each 1 <= k <= n appears k times in the multiset. Terms include rotations/reflections. Related to Latin squares. Inspired by related question in "Chess Set Latin Square" link.
%H Mathematics Stack Exchange, <a href="http://math.stackexchange.com/questions/1136490/chess-set-latin-square">Chess Set Latin Square</a>
%e The a(3) = 5450400 (= 6!*7570) 6 X 6 matrices include
%e 1 2 2 3 3 3
%e 2 1 2 3 3 3
%e 2 2 1 3 3 3
%e 3 3 3 1 2 2
%e 3 3 3 2 1 2
%e 3 3 3 2 2 1.
%e Using terminology such as that suggested by Rebecca J. Stones in a "Chess Set Latin Square" comment, this matrix is a (3, 2, 1)-frequency square corresponding to a decomposition of K_{6,6} into one 3-regular spanning subgraph, one 2-regular spanning subgraph, and one 1-regular spanning subgraph.
%Y Cf. A022915 (includes linear arrangements of same multisets), A000217, A002860.
%K nonn,bref,hard,more
%O 1,2
%A _Rick L. Shepherd_, Feb 28 2016
|
