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A108185 Number of Cantorian n X n matrices over a 2-letter alphabet. 0
0, 4, 24, 1744, 88480, 20785984, 4774925568, 3557583518976, 2784648830636544, 7054995406469377024, 16660711592693252288512 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A matrix is Cantorian if no row matches any of the strings obtained by taking one term from each column in turn in such a way that they are from different rows. That is, no row word can match any transversal word.
More precisely, let the matrix be M = (M_ij). Then no row (M_i1, M_i2, ..., M_in) can agree with any "transversal" (M_{1, pi(1}}, ..., M_{n, pi{n}}) for any permutation pi in S_n.
LINKS
S. Brlek, M. Mendes France, J. M. Robson and M. Rubey, Cantorian tableaux and permanents, L'Enseignement Math. 50 (2004), 287-304.
EXAMPLE
a(2) = 4 because the matrices [[a,a],[b,b]], [[a,b],[b,a]] and the matrices obtained by switching a with b are Cantorian.
CROSSREFS
Sequence in context: A368144 A303131 A012124 * A110972 A065711 A279240
KEYWORD
hard,nonn,nice
AUTHOR
Jeffrey Shallit, Jun 14 2005
STATUS
approved

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Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)