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Transactions of the American Mathematical Society

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


Author: Richard Scott
Journal: Trans. Amer. Math. Soc. 363 (2011), 385-415
MSC (2010): Primary 20F55, 20F10, 05A15
Published electronically: August 30, 2010
MathSciNet review: 2719687
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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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Additional Information

Richard Scott
Affiliation: Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, California 95053
Email: rscott@scu.edu

DOI: https://doi.org/10.1090/S0002-9947-2010-05093-7
Received by editor(s): October 22, 2008
Received by editor(s) in revised form: April 21, 2009
Published electronically: August 30, 2010
Additional Notes: The author thanks MSRI for its support and hospitality during the writing of this paper.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.