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A326342 Number of n X n binary matrices with total support. 2
1, 3, 49, 7443, 6092721 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 9 04:58 EDT 2021. Contains 343687 sequences. (Running on oeis4.)