Rationality and reciprocity for the greedy normal form of a Coxeter group

Scott, Richard

doi:10.1090/S0002-9947-2010-05093-7

Rationality and reciprocity for the greedy normal form of a Coxeter group
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by Richard Scott

Trans. Amer. Math. Soc. 363 (2011), 385-415

DOI: https://doi.org/10.1090/S0002-9947-2010-05093-7

Published electronically: August 30, 2010

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Abstract:

We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series and prove a reciprocity formula for this series when the group is right-angled and the nerve is Eulerian. As corollaries we obtain many of the known rationality and reciprocity results for the growth series of Coxeter groups as well as some new ones.

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