A108185 Number of Cantorian n X n matrices over a 2-letter alphabet.

0, 4, 24, 1744, 88480, 20785984, 4774925568, 3557583518976, 2784648830636544, 7054995406469377024, 16660711592693252288512

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

Table of n, a(n) for n=1..11.

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

Adjacent sequences: A108182 A108183 A108184 * A108186 A108187 A108188

Keyword

hard,nonn,nice

Author

Jeffrey Shallit, Jun 14 2005

Status

approved