Séminaire Lotharingien de Combinatoire, 82B.96 (2019), 12 pp.
Eric Stucky
Cyclic sieving, necklaces, and bracelets
Abstract.
We split the q-Schröder numbers into an "even" and "odd" part. The Schröder numbers are known to enumerate certain necklaces, and the even part turns out to be a q-analogue of the set of bracelets. Both parts are symmetric and unimodal, and we conjecture that there exist posets which explain this phenomenon. Along the way, we find a new cyclic sieving phenomenon on certain double cosets of the symmetric group.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
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