We define and study odd and even analogues of the major index statistics for the classical Weyl groups. More precisely, we show that the generating functions of these statistics, twisted by the one-dimensional characters of the corresponding groups, always factor in an explicit way. In particular, we obtain odd and even analogues of Carlitz's identity, of the Gessel--Simion Theorem, and a parabolic extension, and refinement, of a result of Wachs.

Brenti, F., Sentinelli, P. (2020). Odd and even major indices and one-dimensional characters for classical Weyl groups. ANNALS OF COMBINATORICS, 24(4), 809-835 [10.1007/s00026-020-00515-2].

Odd and even major indices and one-dimensional characters for classical Weyl groups

Brenti F.
;
Sentinelli P.
2020-10-01

Abstract

We define and study odd and even analogues of the major index statistics for the classical Weyl groups. More precisely, we show that the generating functions of these statistics, twisted by the one-dimensional characters of the corresponding groups, always factor in an explicit way. In particular, we obtain odd and even analogues of Carlitz's identity, of the Gessel--Simion Theorem, and a parabolic extension, and refinement, of a result of Wachs.
ott-2020
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/02 - ALGEBRA
English
Con Impact Factor ISI
permutation; major index; Weyl group; generating function; one-dimensional character
https://link.springer.com/content/pdf/10.1007/s00026-020-00515-2.pdf
Brenti, F., Sentinelli, P. (2020). Odd and even major indices and one-dimensional characters for classical Weyl groups. ANNALS OF COMBINATORICS, 24(4), 809-835 [10.1007/s00026-020-00515-2].
Brenti, F; Sentinelli, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/261042
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