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Home > Vol 21, No 4 (2005)

A.M. Hamel¹ and R.C. King²

¹Department of Physics and Computer Science Wilfrid Laurier University Waterloo Ontario N2L 3C5 Canada
²School of Mathematics University of Southampton Southampton SO17 1BJ England

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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