Cyclic Sieving of Matchings

Understand

The cyclic sieving phenomenon (CSP) was introduced by Reiner, Stanton, and White to study combinatorial structures with actions of cyclic groups.

• The crucial step is to find a polynomial, for example a q-analog, that satisfies the CSP conditions for an action.
• This polynomial will give us a lot of information about the symmetry and structure of the set under the action.
• In this paper, we study the cyclic sieving phenomenon of the cyclic group $C_{2n}$ acting on $P_{n,k}$, which is the set of matchings of $2n$ points on a circle with $k$ crossings.