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Search: id:A108185
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| A108185 |
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Number of Cantorian n X n matrices over a 2-letter alphabet. |
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+0
1
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| 0, 4, 24, 1744, 88480, 20785984, 4774925568, 3557583518976, 2784648830636544, 7054995406469377024, 16660711592693252288512
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OFFSET
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1,2
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COMMENT
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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.
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REFERENCES
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S. Brlek, M. Mendes France, J. M. Robson and M. Rubey, Cantorian tableaux and permanents, L'Enseignement Math. 50 (2004), 287-304.
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EXAMPLE
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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.
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CROSSREFS
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Sequence in context: A024251 A024252 A012124 this_sequence A110972 A065711 A077093
Adjacent sequences: A108182 A108183 A108184 this_sequence A108186 A108187 A108188
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KEYWORD
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hard,nonn,nice
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AUTHOR
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Jeffrey Shallit (shallit(AT)graceland.uwaterloo.ca), Jun 14 2005
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