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- Alexandersson, Per, et al.
(författare)
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The cyclic sieving phenomenon on circular Dyck paths
- 2019
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Ingår i: The Electronic Journal of Combinatorics. - : ELECTRONIC JOURNAL OF COMBINATORICS. - 1097-1440 .- 1077-8926. ; 26:4
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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