Expressions for Catalan Kronecker Products
Andrew Brown, Stephanie van Willigenburg, Mike Zabrocki
TL;DR
This paper presents elementary positive formulas for specific Catalan Kronecker products, revealing fundamental properties of Kronecker coefficients and enabling new enumerative and combinatorial insights.
Contribution
It introduces new explicit positive formulas for certain Catalan Kronecker products, advancing understanding of their combinatorial structure.
Findings
Elementary positive formulas for specific Kronecker products
Demonstration of fundamental properties of Kronecker coefficients
Derivation of enumerative and combinatorial results
Abstract
We give some elementary manifestly positive formulae for the Kronecker products s_(d,d) * s_(d+k,d-k) and s_(d,d) * s_(2d-k,1^k). These formulae demonstrate some fundamental properties of the Kronecker coefficients, and we use them to deduce a number of enumerative and combinatorial results.
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