A354741 -id:A354741 - cp's OEIS frontend

A355333 Triangle read by rows: T(n,k) is the number of n X n Boolean matrices with Schein rank k, 0 <= k <= n.

1, 1, 1, 1, 9, 6, 1, 49, 306, 156, 1, 225, 8550, 40656, 16104, 1, 961, 194850, 5771100, 21165720, 6421800

Offset: 0

Pontus von Brömssen, Jun 29 2022

Also, T(n,k) is the number of spanning subgraphs of the complete bipartite graph K_{n,n} that have bipartite dimension (or biclique covering number) k.

			Triangle begins:
  n\k | 0   1      2       3        4       5
  ----+--------------------------------------
   0  | 1
   1  | 1   1
   2  | 1   9      6
   3  | 1  49    306     156
   4  | 1 225   8550   40656    16104
   5  | 1 961 194850 5771100 21165720 6421800

Mathematics Stack Exchange, Calculating the rank of a Boolean matrix and Boolean matrix factorization
Wikipedia, Bipartite dimension
Wikipedia, Boolean matrix

Cf. A002416 (row sums), A064230, A286331, A354741, A355334.

A363036 Triangular array read by rows. T(n,k) is the number of regular elements in the semigroup of all binary relations on [n] that have rank k, n>=0, 0<=k<=n.

Original entry on oeis.org

1, 1, 1, 1, 9, 6, 1, 49, 306, 114, 1, 225, 8550, 26376, 5256, 1, 961, 194850, 3311250, 4669200, 507720

Offset: 0

Geoffrey Critzer, May 17 2023

			 1;
 1,   1;
 1,   9,      6;
 1,  49,    306,     114;
 1, 225,   8550,   26376,    5256;
 1, 961, 194850, 3311250, 4669200, 507720;
 ...

K. K.-H. Butler and G. Markowsky, The Number of Maximal Subgroups of the Semigroup of Binary Relations, Kyungpook Math. J. Vol 12, June 1972.

Cf. A354279 (row sums), A003425 (main diagonal), A060867 (column k=1), A354741.

cp's OEIS Frontend

A355333 Triangle read by rows: T(n,k) is the number of n X n Boolean matrices with Schein rank k, 0 <= k <= n.

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