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Cyclic sieving for two families of non-crossing graphs

Abstract : We prove the cyclic sieving phenomenon for non-crossing forests and non-crossing graphs. More precisely, the cyclic group acts on these graphs naturally by rotation and we show that the orbit structure of this action is encoded by certain polynomials. Our results confirm two conjectures of Alan Guo.
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Svetlana Poznanović. Cyclic sieving for two families of non-crossing graphs. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.789-800, ⟨10.46298/dmtcs.2953⟩. ⟨hal-01215075⟩

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