ALGEBRAIC COMBINATORICS

no. 6
Odd length in Weyl groups
Brenti, Francesco1; Carnevale, Angela2
1 Dipartimento di Matematica Università di Roma “Tor Vergata” Via della Ricerca Scientifica, 1 00133 Roma, Italy
2 Fakultät für Mathematik Universität Bielefeld Postfach 100131 D-33501 Bielefeld, Germany
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:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.69
Classification: 17B22, 20F55, 05E99
Keywords: Root system, Weyl group, Coxeter group, odd length, enumeration.
Brenti, Francesco 1; Carnevale, Angela 2

1 Dipartimento di Matematica Università di Roma “Tor Vergata” Via della Ricerca Scientifica, 1 00133 Roma, Italy
2 Fakultät für Mathematik Universität Bielefeld Postfach 100131 D-33501 Bielefeld, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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/articles/10.5802/alco.69/

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