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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS 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. 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

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Last modified October 14 20:08 EDT 2019. Contains 328022 sequences. (Running on oeis4.)