Odd length in Weyl groups
Abstract
We define a new statistic on any Weyl group which we call the odd length and which reduces, for Weyl groups of types $A$, $B$, and $D$, the the statistics by the same name that have already been defined and studied in [10], [13], [14], and [3]. We show that the signed (by length) generating function of the odd length always factors nicely except possibly in type $E_8$, and we obtain multivariate analogues of these factorizations in types $B$ and $D$.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2017
- DOI:
- 10.48550/arXiv.1709.03320
- arXiv:
- arXiv:1709.03320
- Bibcode:
- 2017arXiv170903320B
- Keywords:
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- Mathematics - Combinatorics