Bounded Littlewood identity related to alternating sign matrices
Forum of Mathematics, Sigma, Tome 12 (2024)
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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 mysterious relation between alternating sign trapezoids and plane partition objects.
@article{10_1017_fms_2024_70,
author = {Ilse Fischer},
title = {Bounded {Littlewood} identity related to alternating sign matrices},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {12},
year = {2024},
doi = {10.1017/fms.2024.70},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.70/}
}
Ilse Fischer. Bounded Littlewood identity related to alternating sign matrices. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.70
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