The Cyclic Sieving Phenomenon for non-crossing forests
Stefan Kluge
TL;DR
This paper proves that non-crossing forests, under rotation, exhibit the cyclic sieving phenomenon with a natural q-analogue, confirming a conjecture by Alan Guo.
Contribution
It establishes the cyclic sieving phenomenon for non-crossing forests with a natural q-analogue, confirming a conjecture by Alan Guo.
Findings
Cyclic sieving phenomenon holds for non-crossing forests
A natural q-analogue formula for their count is identified
Conjecture by Alan Guo is proven
Abstract
In this paper we prove that the set of non-crossing forests together with a cyclic group acting on it by rotation and a natural q-analogue of the formula for their number exhibits the cyclic sieving phenomenon, as conjectured by Alan Guo.
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