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 , , and , 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 and .
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.69
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}, pages = {1125--1147}, publisher = {MathOA foundation}, volume = {2}, number = {6}, year = {2019}, doi = {10.5802/alco.69}, mrnumber = {4049840}, zbl = {07140427}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.69/} }
Brenti, Francesco; Carnevale, Angela. Odd length in Weyl groups. Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1125-1147. doi : 10.5802/alco.69. http://www.numdam.org/articles/10.5802/alco.69/
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