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$Poincar\'{e}$ Series of Subsets of Affine Weyl Groups

Viswanath, Sankaran (2008) $Poincar\'{e}$ Series of Subsets of Affine Weyl Groups. In: Proceedings of the American Mathematical Society, 136 (11). pp. 3735-3740.

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In this note, we identify a natural class of subsets of affine Weyl groups whose $Poincar\'{e}$ series are rational functions. This class includes the sets of minimal coset representatives of reflection subgroups. As an application, we construct a generalization of the classical length-descent generating function and prove its rationality.

Item Type: Journal Article
Publication: Proceedings of the American Mathematical Society
Publisher: American Mathematical Society
Additional Information: Copyright of this article belongs to American Mathematical Society.
Keywords: Rational function;descent;reflection subgroup.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 18 Oct 2008 05:43
Last Modified: 19 Sep 2010 04:50
URI: http://eprints.iisc.ac.in/id/eprint/16126

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