U-turn Alternating Sign Matrices, Symplectic Shifted Tableaux and Their Weighted Enumeration

Details U-turn Alternating Sign Matrices, Symplectic Shifted Tableaux and Their Weighted Enumeration U-turn Alternating Sign Matrices, Symplectic Shifted Tableaux and Their Weighted Enumeration

2003-12-08

arxiv.org/abs/math/0312169v1

Mathematics

Combinatorics

25 pages

Scientific paper

Alternating sign matrices with a U-turn boundary (UASMs) are a recent generalization of ordinary alternating sign matrices. Here we show that variations of these matrices are in bijective correspondence with certain symplectic shifted tableaux that were recently introduced in the context of a symplectic version of Tokuyama's deformation of Weyl's denominator formula. This bijection yields a formula for the weighted enumeration of UASMs. In this connection use is made of the link between UASMs and certain square ice configuration matrices.

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