ALGEBRAIC COMBINATORICS

no. 6
Odd length in Weyl groups
Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1125-1147.

We define for any crystallographic root system a new statistic on the corresponding Weyl group which we call the odd length. This statistic reduces, for Weyl groups of types A, B, and D, to the each of the statistics by the same name that have already been defined and studied in [8], [12], [13], and [3]. We show that the sign-twisted generating function of the odd length always factors completely, and we obtain multivariate analogues of these factorizations in types B and D.

Received: 2018-08-19
Revised: 2019-02-28
Accepted: 2019-03-02
Published online: 2019-12-04
DOI: https://doi.org/10.5802/alco.69
Classification: 17B22 20F55 05E99
Keywords: Root system, Weyl group, Coxeter group, odd length, enumeration. 
@article{ALCO_2019__2_6_1125_0,
     author = {Brenti, Francesco and Carnevale, Angela},
     title = {Odd length in Weyl groups},
     journal = {Algebraic Combinatorics},
     publisher = {MathOA foundation},
     volume = {2},
     number = {6},
     year = {2019},
     pages = {1125-1147},
     doi = {10.5802/alco.69},
     mrnumber = {4049840},
     zbl = {07140427},
     language = {en},
     url = {alco.centre-mersenne.org/item/ALCO_2019__2_6_1125_0/}
}
Brenti, Francesco; Carnevale, Angela. Odd length in Weyl groups. Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1125-1147. doi : 10.5802/alco.69. https://alco.centre-mersenne.org/item/ALCO_2019__2_6_1125_0/

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