Bounds On Schubert Coefficients in the Two-Row Case

TL;DR

This paper establishes an upper bound for specific Littlewood-Richardson coefficients associated with two-row Young diagrams and Grassmannian permutations, contributing to the understanding of Schubert calculus.

Contribution

It introduces a new upper bound for generalized Littlewood-Richardson coefficients in the two-row case and proposes a conjecture for broader bounds.

Findings

Derived an explicit upper bound for two-row Young diagram coefficients

Connected bounds to Grassmannian permutations

Proposed a conjecture for general structure constants

Abstract

Weprovide an upper bound for generalized Littlewood-Richardson coefficients $c^w_{uv}$, where $u$ is a two-row Young diagram corresponding to a Grassmannian permutation. We end with a conjecture on the upper bounds for all such structure constants.