A326343 - OEIS

A326343

Number of inequivalent n X n binary matrices with total support, where equivalence means permutations of rows or columns.

1, 2, 6, 42, 894, 62350

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OFFSET

1,2

COMMENTS

A nonnegative matrix has total support if it is nonzero and for every positive entry there exists a permutation of the columns such that the positive entry is a diagonal entry afterwards and all diagonal entries are positive afterwards.

Number of inequivalent n X n binary matrices generated by applying the sign function on the entries of a doubly stochastic n X n matrix. - [R. Sinkhorn and P. Knopp (1967)]

LINKS

Table of n, a(n) for n=1..6.

Priyanka Karmakar, Hariram Krishna, Souvik Pal, and G. Krishna Teja, Characterization of Erdős matrices by their zero entries, arXiv:2512.04766 [math.CO], 2025. See p. 9.

Paul Knopp and Richard Sinkhorn, Concerning nonnegative matrices and doubly stochastic matrices, Pacific J. Math., Vol. 21, No. 2 (1967), 343-348.

Christian Stricker, All such matrices for n = 3.

Christian Stricker, All such matrices for n = 4.

Christian Stricker, All such matrices for n = 5.

EXAMPLE

For n = 2 the a(2) = 2 matrices are:

[1 1] [1 0]

[1 1], [0 1].

CROSSREFS

A326342 additionally considers equivalent matrices.

Sequence in context: A294349 A325782 A374891 * A276453 A152479 A250309

Adjacent sequences: A326340 A326341 A326342 * A326344 A326345 A326346

KEYWORD

nonn,more

AUTHOR

Christian Stricker, Jun 28 2019

STATUS

approved