The On-Line Encyclopedia of Integer Sequences (OEIS)

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A104602

Number of square (0,1)-matrices with exactly n entries equal to 1 and no zero row or columns.
(history; published version)

#27 by Susanna Cuyler at Thu Nov 15 08:39:50 EST 2018

STATUS

proposed

approved

#26 by Michel Marcus at Thu Nov 15 02:08:31 EST 2018

STATUS

editing

proposed

#25 by Michel Marcus at Thu Nov 15 02:08:29 EST 2018

LINKS

H. Cheballah, S. Giraudo, R. Maurice, <a href="http://arxiv.org/abs/1306.6605">Combinatorial Hopf algebra structure on packed square matrices</a>, arXiv preprint arXiv:1306.6605, [math.CO], 2013-2015.

M. Maia and M. Mendez, <a href="httphttps://arXivarxiv.org/abs/math.CO/0503436">On the arithmetic product of combinatorial species</a>, arXiv:math/0503436 [math.CO], 2005.

STATUS

proposed

editing

#24 by Gus Wiseman at Wed Nov 14 20:47:06 EST 2018

STATUS

editing

proposed

#23 by Gus Wiseman at Wed Nov 14 20:03:29 EST 2018

EXAMPLE

From Gus Wiseman, Nov 14 2018: (Start)

The a(3) = 10 matrices:

[1 1] [1 1] [1 0] [0 1]

[1 0] [0 1] [1 1] [1 1]

.

[1 0 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1] [0 0 1]

[0 1 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [0 1 0]

[0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]

(End)

MATHEMATICA

Table[Length[Select[Subsets[Tuples[Range[n], 2], {n}], Union[First/@#]==Union[Last/@#]==Range[Max@@First/@#]&]], {n, 5}] (* Gus Wiseman, Nov 14 2018 *)

CROSSREFS

Cf. A048291, A049311, A054976, A057150, A057151, A101370, A120732, A120733, A138178, A316983, A319616.

STATUS

approved

editing

#22 by Paul D. Hanna at Mon Mar 26 01:06:39 EDT 2018

STATUS

editing

approved

#21 by Paul D. Hanna at Mon Mar 26 01:06:37 EDT 2018

FORMULA

G.f.: Sum_{n>=0} ((1+x)^n - 1)^n / (1+x)^(n*(n+1)). - Paul D. Hanna, Mar 26 2018

STATUS

approved

editing

#20 by Paul D. Hanna at Mon Mar 26 00:36:06 EDT 2018

STATUS

editing

approved

#19 by Paul D. Hanna at Mon Mar 26 00:36:04 EDT 2018

FORMULA

G.f.: ((1+x)^n - 1)^n / (1+x)^(n*(n+1)). - Paul D. Hanna, Mar 26 2018

STATUS

approved

editing

#18 by Vaclav Kotesovec at Sun May 03 05:16:10 EDT 2015

STATUS

editing

approved