A326342 Number of n X n binary matrices with total support.

1, 3, 49, 7443, 6092721

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 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..5.

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

Example

For n = 2 the a(2) = 3 matrices are:
  [1 1]  [1 0]  [0 1]
  [1 1], [0 1], [1 0].

Crossrefs

A326343 counts only the inequivalent matrices.

Sequence in context: A203743 A086459 A180602 * A203700 A063893 A291707

Adjacent sequences: A326339 A326340 A326341 * A326343 A326344 A326345

Keyword

nonn,more

Author

Christian Stricker, Jun 28 2019

Status

approved