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Preprints, Working Papers, ... Year : 2024

Generalised core partitions and Diophantine equations


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


  • HAL Id : hal-04507916 , version 1


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