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The cyclic sieving phenomenon on circular Dyck paths
Stockholm Univ, Dept Math, Stockholm, Sweden..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6339-2230
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-4489-1920
2019 (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
ELECTRONIC JOURNAL OF COMBINATORICS , 2019. Vol. 26, no 4, article id P4.16
National Category
Mathematics
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URN: urn:nbn:se:kth:diva-263345ISI: 000489745700016Scopus ID: 2-s2.0-85074038172OAI: oai:DiVA.org:kth-263345DiVA, id: diva2:1371371
Note

QC 20191119

Available from: 2019-11-19 Created: 2019-11-19 Last updated: 2019-11-19Bibliographically approved

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