The poset perspective on alternating sign matrices

Details The poset perspective on alternating sign matrices The poset perspective on alternating sign matrices

2009-05-27

arxiv.org/abs/0905.4495v1

Mathematics

Combinatorics

10 pages, to appear in DMTCS as part of the conference proceedings for FPSAC 2009

Scientific paper

Alternating sign matrices (ASMs) are square matrices with entries 0, 1, or -1 whose rows and columns sum to 1 and whose nonzero entries alternate in sign. We put ASMs into a larger context by studying the order ideals of subposets of a certain poset, proving that they are in bijection with a variety of interesting combinatorial objects, including ASMs, totally symmetric self--complementary plane partitions (TSSCPPs), Catalan objects, tournaments, semistandard Young tableaux, and totally symmetric plane partitions. We use this perspective to prove an expansion of the tournament generating function as a sum over TSSCPPs which is analogous to a known formula involving ASMs.

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