Coxeter-biCatalan combinatorics

Coxeter-biCatalan combinatorics We pose counting problems related to the various settings for Coxeter-Catalan combinatorics (noncrossing, nonnesting, clusters, Cambrian). Each problem is to count “twin” pairs of objects from a corresponding problem in Coxeter-Catalan combinatorics. We show that the problems all have the same answer, and, for a given finite Coxeter group W, we call the common solution to these problems the W-biCatalan number. We compute the W-biCatalan number for all W and take the first steps in the study of Coxeter-biCatalan combinatorics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Algebraic Combinatorics Springer Journals

Coxeter-biCatalan combinatorics

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Combinatorics; Convex and Discrete Geometry; Order, Lattices, Ordered Algebraic Structures; Computer Science, general; Group Theory and Generalizations
ISSN
0925-9899
eISSN
1572-9192
D.O.I.
10.1007/s10801-017-0775-1
Publisher site
See Article on Publisher Site

Abstract

We pose counting problems related to the various settings for Coxeter-Catalan combinatorics (noncrossing, nonnesting, clusters, Cambrian). Each problem is to count “twin” pairs of objects from a corresponding problem in Coxeter-Catalan combinatorics. We show that the problems all have the same answer, and, for a given finite Coxeter group W, we call the common solution to these problems the W-biCatalan number. We compute the W-biCatalan number for all W and take the first steps in the study of Coxeter-biCatalan combinatorics.

Journal

Journal of Algebraic CombinatoricsSpringer Journals

Published: Aug 10, 2017

References

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