Generalised core partitions and Diophantine equations - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2024

Generalised core partitions and Diophantine equations

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.
Fichier principal
Vignette du fichier
coresizes.pdf (1.41 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Licence : CC BY - Attribution

Dates and versions

hal-04507916 , version 1 (17-03-2024)

Identifiers

  • HAL Id : hal-04507916 , version 1

Cite

Olivier Brunat, Nathan Chapelier-Laget, Thomas Gerber. Generalised core partitions and Diophantine equations. 2024. ⟨hal-04507916⟩
2 View
1 Download

Share

Gmail Facebook X LinkedIn More