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

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.

R. Sinkhorn and P. Knopp, Concerning nonnegative matrices and doubly stochastic matrices, Pacific Journal of Mathematics, 21(2):343-348, 1967.

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: A270141 A294349 A325782 * A276453 A152479 A250309

Adjacent sequences: A326340 A326341 A326342 * A326344 A326345 A326346

Keyword

nonn,more

Author

Christian Stricker, Jun 28 2019

Status

approved