Refined Catalan and Narayana cyclic sieving

We prove several new instances of the cyclic sieving phenomenon (CSP) on Catalan objects of type A and type B. Moreover, we refine many of the known instances of the CSP on Catalan objects. For example, we consider triangulations refined by the number of "ears", non-crossing matchings with...

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Published in:arXiv.org 2020-11
Main Authors: Alexandersson, Per, Linusson, Svante, Potka, Samu, Uhlin, Joakim
Format: Article
Language:English
Online Access:Get full text
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Summary:We prove several new instances of the cyclic sieving phenomenon (CSP) on Catalan objects of type A and type B. Moreover, we refine many of the known instances of the CSP on Catalan objects. For example, we consider triangulations refined by the number of "ears", non-crossing matchings with a fixed number of short edges, and non-crossing configurations with a fixed number of loops and edges.
ISSN:2331-8422
DOI:10.48550/arxiv.2010.11157