The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A354741

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A354741

Triangular array read by rows. T(n,k) is the number of n X n Boolean matrices with row rank k, n >= 0, 0 <= k <= n.
(history; published version)

#44 by Alois P. Heinz at Thu Jul 14 08:57:40 EDT 2022

STATUS

proposed

approved

#43 by Pontus von Brömssen at Thu Jul 14 08:42:45 EDT 2022

STATUS

editing

proposed

Discussion

Thu Jul 14

08:57

Alois P. Heinz: thanks ...

#42 by Pontus von Brömssen at Thu Jul 14 08:40:20 EDT 2022

DATA

1, 1, 1, 1, 9, 6, 1, 49, 306, 156, 1, 225, 8550, 37488, 19272, 1, 961, 194850, 4811700, 17551800, 10995120

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/Bipartite_dimension">Bipartite dimension</a>

CROSSREFS

Cf. A048651, A064230, A286331, A355333.

EXTENSIONS

Row n=5 from Pontus von Brömssen, Jul 14 2022

STATUS

approved

editing

Discussion

Thu Jul 14

08:42

Pontus von Brömssen: In my earlier attempt to compute this sequence, it turned out that I was actually computing the Schein rank, not the row-rank as defined here. The corresponding sequence for Schein rank is now A355333. It's the Schein rank that is related to bipartite dimension, so I deleted that link from this sequence.

#41 by Alois P. Heinz at Mon Jun 20 15:38:49 EDT 2022

STATUS

proposed

approved

#40 by Pontus von Brömssen at Mon Jun 20 14:42:58 EDT 2022

STATUS

editing

proposed

Discussion

Mon Jun 20

14:45

Pontus von Brömssen: I should have said "the first *three* terms of row 4".

15:38

Alois P. Heinz: ok, thanks ...

#39 by Pontus von Brömssen at Mon Jun 20 14:41:52 EDT 2022

COMMENTS

T(n,k) is the number of spanning subgraphs of the complete bipartite graph K_{n,n} that have bipartite dimension k. - Pontus von Brömssen, Jun 18 2022

STATUS

approved

editing

Discussion

Mon Jun 20

14:42

Pontus von Brömssen: I remove my comment for now, because the values I get when I use it does not match the given ones. The results match up to row 3 and the first two terms of row 4, but then I get T(4,3)=40656 and T(4,4)=16104. I'll try to figure out if there's a bug in my code, if my comment is incorrect, or if I misinterpreted the definition of this sequence. Here's a relevant question on stackexchange: https://math.stackexchange.com/questions/1345231/ .

#38 by Michael De Vlieger at Sun Jun 19 12:48:56 EDT 2022

STATUS

reviewed

approved

#37 by Joerg Arndt at Sun Jun 19 10:23:00 EDT 2022

STATUS

proposed

reviewed

#36 by Michel Marcus at Sun Jun 19 10:09:42 EDT 2022

STATUS

editing

proposed

Discussion

Sun Jun 19

10:23

Joerg Arndt: "limiting probability --> 1" is not quite unexpected: the image of the canonical basis vector e_i is mapped to the nullvector only if *all* entries of column i are zeros.

#35 by Michel Marcus at Sun Jun 19 10:09:34 EDT 2022

COMMENTS

Compare to A286331 which counts n X n matrices over the field GF(2). Note that the n -> infinity limit when n->oo of the probability that a matrix over GF(2) has rank n is equal to Product_{i>=1} (1-1/2^i) = 0.288... (see A048651). Here, it appears (from some empirical computations) that the limiting probability that a Boolean matrix has rank n is 1.

STATUS

proposed

editing