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

Author

Pontus von Brömssen, Jun 29 2022

Keywords

• nonn
• tabl
• more

Comments

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.

Examples

			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
		

Links

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

Crossrefs

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