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arXiv · 2301.00175

Bounded Littlewood identity related to alternating sign matrices

Ilse Fischer
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Abstract

An identity that is reminiscent of the Littlewood identity plays a fundamental role in recent proofs of the facts that alternating sign triangles are equinumerous with totally symmetric self-complementary plane partitions and that alternating sign trapezoids are equinumerous with holey cyclically symmetric lozenge tilings of a hexagon. We establish a bounded version of a generalization of this identity. Further, we provide combinatorial interpretations of both sides of the identity. The ultimate goal would be to construct a combinatorial proof of this identity (possibly via an appropriate variant of the Robinson-Schensted-Knuth correspondence) and its unbounded version as this would improve the understanding of the relation between alternating sign trapezoids and plane partition objects.

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Ilse Fischer. 2022-12-31. Bounded Littlewood identity related to alternating sign matrices. https://doi.org/10.1017/fms.2024.70

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