1,2

A wide partition is a partition with the property that any sub-partition (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.

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. 334-358.

T. Chow, C. Fan, M. Goemans, J. Vondrak, Wide Partitions, Latin Tableaux, and Rota's Basis Conjecture.

If a wide partition has its first part of size n, then it has to fit in an n-by-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.

Sequence in context: A079121 A027077 A052855 this_sequence A080923 A118264 A006365

Adjacent sequences: A133784 A133785 A133786 this_sequence A133788 A133789 A133790

hard,more,nonn

Paul Raff (praff(AT)math.rutgers.edu), Jan 02 2008