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The cyclic sieving phenomenon on circular Dyck paths
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 32019 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 26, no 4, article id P4.16Article in journal (Refereed) Published
Abstract [en]

We give a q-enumeration of circular Dyck paths, which is a superset of the classical Dyck paths enumerated by the Catalan numbers. These objects have recently been studied by Alexandersson and Panova. Furthermore, we show that this q-analogue exhibits the cyclic sieving phenomenon under a natural action of the cyclic group. The enumeration and cyclic sieving is generalized to Mobius paths. We also discuss properties of a generalization of cyclic sieving, which we call subset cyclic sieving, and introduce the notion of Lyndon-like cyclic sieving that concerns special recursive properties of combinatorial objects exhibiting the cyclic sieving phenomenon.

Place, publisher, year, edition, pages
2019. Vol. 26, no 4, article id P4.16
National Category
Mathematics
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URN: urn:nbn:se:su:diva-175801ISI: 000489745700016OAI: oai:DiVA.org:su-175801DiVA, id: diva2:1372521
Available from: 2019-11-25 Created: 2019-11-25 Last updated: 2019-11-25Bibliographically approved

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