New partition identities for odd w odd

2023/01/29 by Mirko Primc, Primc, Mirko · 1 citation
Mathematics · #05A19 (Primary) 17B67 (Secondary) #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2301.12484

openalex publication_date 2023/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this note we conjecture Rogers-Ramanujan type colored partition identities for an array with odd number of rows w such that the first and the last row consist of even positive integers. In a strange way this is different from the partition identities for the array with odd number of rows w such that the first and the last row consist of odd positive integers -- the partition identities conjectured by S. Capparelli, A. Meurman, A. Primc and the author and related to standard representations of the affine Lie algebra of type C⁽¹⁾_ℓ for w=2ℓ+1. The conjecture is based on numerical evidence.

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• Affine Jacobi-Trudi formulas and q,t-Rogers-Ramanujan identities

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