Atomic length on Weyl groups - Archive ouverte HAL
Article Dans Une Revue Journal of Combinatorial Algebra Année : 2024

Atomic length on Weyl groups

Résumé

We define a new statistic on Weyl groups called the atomic length and investigate its combinatorial and representation-theoretic properties. In finite types, we show a number of properties of the atomic length which are reminiscent of the properties of the usual length. Moreover, we prove that, with the exception of rank two, this statistic describes an interval. In affine types, our results shed some light on classical enumeration problems, such as the celebrated Granville-Ono theorem on the existence of core partitions, by relating the atomic length to the theory of crystals.
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Dates et versions

hal-03866168 , version 1 (22-11-2022)
hal-03866168 , version 2 (15-12-2022)

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Nathan Chapelier-Laget, Thomas Gerber. Atomic length on Weyl groups. Journal of Combinatorial Algebra, In press. ⟨hal-03866168v2⟩
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