

A326342


Number of n X n binary matrices with total support.


2




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):343348, 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



