Factorization of certain Macdonald Littlewood-Richardson coefficients

2023/01/16 by Konstantin I. Matveev, Yuchen Wei, Matveev, Konstantin +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2301.06500

Abstract

We find and prove a factorization formula for certain Macdonald Littlewood-Richardson coefficients c_λμ^ν(q,t). Namely, we consider the case that the Kostka number K_{μ, ν-λ} is 1. This settles a particular case of a more general conjecture of Richard Stanely. This conjecture proposes that a factorization formula exists whenever the corresponding regular Littlewood-Richardson coefficient c^ν_λμ is 1.

Related

• Factorization formulas for Macdonald polynomials
• Littlewood-Richardson coefficients as a signed sum of Kostka numbers
• The computation of Kostka Numbers and Littlewood-Richardson Coefficients is #P-complete
• Bidilatation of Small Littlewood-Richardson Coefficients
• Geometric Proof of a Conjecture of King, Tollu, and Toumazet