Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On enumeration of conjugacy classes of Coxeter elements


Authors: Matthew Macauley and Henning S. Mortveit
Journal: Proc. Amer. Math. Soc. 136 (2008), 4157-4165
MSC (2000): Primary 20F55, 05A99, 06A06
Published electronically: June 20, 2008
Erratum: Proc. Amer. Math. Soc. 137 (2009), 3167
MathSciNet review: 2431028
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study the equivalence relation on the set of acyclic orientations of a graph $ Y$ that arises through source-to-sink conversions. This source-to-sink conversion encodes, e.g. conjugation of Coxeter elements of a Coxeter group. We give a direct proof of a recursion for the number of equivalence classes of this relation for an arbitrary graph $ Y$ using edge deletion and edge contraction of non-bridge edges. We conclude by showing how this result may also be obtained through an evaluation of the Tutte polynomial as $ T_Y(1,0)$, and we provide bijections to two other classes of acyclic orientations that are known to be counted in the same way. A transversal of the set of equivalence classes is given.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20F55, 05A99, 06A06

Retrieve articles in all journals with MSC (2000): 20F55, 05A99, 06A06


Additional Information

Matthew Macauley
Affiliation: Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93106-3080 – and – NDSSL, Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, Virginia 24061
Address at time of publication: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634 - and - NDSSL, Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, Virginia 24061
Email: macauley@vt.edu, mmacaul@clemson.edu

Henning S. Mortveit
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061 – and – NDSSL, Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, Virginia 24061
Email: henning.mortveit@vt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09543-9
PII: S 0002-9939(08)09543-9
Received by editor(s): November 7, 2007
Published electronically: June 20, 2008
Communicated by: Jim Haglund
Article copyright: © Copyright 2008 American Mathematical Society