A355333 - OEIS

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

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OFFSET

0,5

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.

LINKS

Table of n, a(n) for n=0..20.

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

Wikipedia, Bipartite dimension

Wikipedia, Boolean matrix

EXAMPLE

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

CROSSREFS

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

Sequence in context: A286331 A363036 A354741 * A089479 A269444 A199431

Adjacent sequences: A355330 A355331 A355332 * A355334 A355335 A355336

KEYWORD

nonn,tabl,more

AUTHOR

Pontus von Brömssen, Jun 29 2022

STATUS

approved