Geometric Proof of a Conjecture of King, Tollu, and Toumazet

Abstract

In their 2004 paper, Stretched Littlewood-Richardson and Kostka Coefficients, King, Tollu, and Toumazet conjectured that if a Littlewood-Richardson coefficient of value 2 is stretched by a factor of N, the resulting coefficient has value N+1. A generalization of this is proven using geometric methods and Schubert calculus.

arXiv comment20 pages. Minor improvements have been made throughout in the latest version, and a significant error from previous versions has been corrected