Generalised core partitions and Diophantine equations

2024/03/17 by Olivier Brunat, Brunat, Olivier, Nathan Chapelier‐Laget +3
Computer Science · Mathematics · #05E10 #11D09 #17B22 #17B67 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2403.11191

openalex publication_date 2024/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study generalised core partitions arising from affine Grassmannian elements in arbitrary Dynkin type. The corresponding notion of size is given by the atomic length in the sense of [CLG22]. In this paper, we first develop the theory for extended affine Weyl groups. In a series of applications, we give some remarkable parametrisations of the solutions of certain Diophantine equations resembling Pell's equation, by refining the results of [BN22] and [Alp14], and generalising them to further types.

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• Strange Expectations in Affine Weyl Groups
• Affine Symmetries for ABJM Partition Function and its Generalization
• Results and conjectures on simultaneous core partitions