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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Counting equivalence classes of vertex pairs modulo the dihedral action on the associahedron


Authors: Douglas Bowman and Alon Regev
Journal: Proc. Amer. Math. Soc. 141 (2013), 779-789
MSC (2010): Primary 05C30, 32B25, 52B11, 52B15, 52B05, 05E18
Published electronically: July 12, 2012
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Abstract: This paper proves explicit formulae for the number of edges, $ 2$-sets and diagonals in the associahedron of dimension $ n$ modulo the action of the dihedral group. A generating function for the number of $ k$-sets modulo this action, as well as a formula for the cycle index, is given. A table of values is also provided.


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Additional Information

Douglas Bowman
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115
Email: bowman@math.niu.edu

Alon Regev
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115
Email: regev@math.niu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11626-0
PII: S 0002-9939(2012)11626-0
Received by editor(s): February 17, 2011
Received by editor(s) in revised form: July 17, 2011
Published electronically: July 12, 2012
Communicated by: Jim Haglund
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.