

A133787


Number of wide partitions whose first part is of size n.


0



1, 3, 8, 24, 71, 226, 718, 7860, 26669, 91152, 316194, 1103506, 3892806, 13803606, 43946652
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OFFSET

1,2


COMMENTS

A wide partition is a partition with the property that any subpartition (meaning, a partition obtained by taking some of the parts) dominates its conjugate.
A special case of Rota's Basis Conjecture is a generalization of the Dinitz Conjecture, namely that there is a diagram  a Young Tableaux such that you see 1 through n in each row of size n and at most one of each digit in each column  if and only if the partition is wide.


LINKS

Table of n, a(n) for n=1..15.
T. Chow, C. Fan, M. Goemans, J. Vondrak, Wide Partitions, Latin Tableaux and Rota's Basis Conjecture, Advances in Applied Mathematics, Vol. 31 (2003), No. 2, pp. 334358.


EXAMPLE

If a wide partition has its first part of size n, then it has to fit in an n X n grid, or it itself does not dominate its conjugate. a(2) is equal to 3 because {2}, {2,1} and {2,2} are all wide partitions.


CROSSREFS

Sequence in context: A291243 A153774 A052855 * A080923 A118264 A006365
Adjacent sequences: A133784 A133785 A133786 * A133788 A133789 A133790


KEYWORD

hard,more,nonn


AUTHOR

Paul Raff, Jan 02 2008


STATUS

approved



