Bounded Littlewood identity related to alternating sign matrices

Bounded Littlewood identity related to alternating sign matrices

Blog Article

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 Foundation 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 CITRUS SOAP 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.