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Cyclic sieving phenomena via combinatorics of continued fractions
Bishal Deb
https://arxiv.org/abs/2508.13709 https://arxiv.org/pdf/2508.13709

Cyclic sieving phenomena via combinatorics of continued fractions
We will exhibit several instances of the cyclic sieving phenomenon involving statistics and involutions on the following combinatorial families of objects: permutations, set partitions, perfect matchings, D-permutations (and its subclasses). Our results will be based on continued fraction identities enumerating these objects. Our instances of cyclic sieving phenomenon for permutations involve the Corteel involution; this was first studied by Adams, Elder, Lafrenière, McNicholas, Striker and We…