A Littlewood-type identity for Robbins polynomials
Abstract
We provide a generalization of the Littlewood identity, both sides of which are related to alternating sign matrices. The classical Littlewood identity establishes a nice product formula for the sum of all Schur polynomials. Compared to the classical identity, Schur polynomials are replaced by so-called modified Robbins polynomials . These polynomials are a generalization of Schur polynomials and enumerate down-arrowed monotone triangles , and thus also alternating sign matrices. As an additional factor on the other side of the identity, we have a Pfaffian formula which we interpret in terms of the partition function of six-vertex model configurations corresponding to diagonally symmetric alternating sign matrices .
Fields of Study & Subjects
Meromorphic and Entire Functions
Advanced Combinatorial Mathematics
Mathematics and Applications
Publication details
- Journal / source
- Algebraic Combinatorics
- Volume
- 9
- Issue
- 3
- Pages
- 665–700
- Publication date
- 1 July 2026
- Language
- EN