Cyclic sieving for two families of non-crossing graphs

• Main Author: Poznanović, Svetlana
• Other Authors: School of Mathematics - Georgia Institute of Technology, Georgia Institute of Technology Atlanta, Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2011
• Subjects: cyclic sieving; non-crossing forests; non-crossing graphs; [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]; [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]; Iceland
• Online Access: https://hal.inria.fr/hal-01215075; https://hal.inria.fr/hal-01215075/document; https://hal.inria.fr/hal-01215075/file/dmAO0169.pdf

International audience 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. Nous prouvons le phénomène de crible cyclique pour les forêts et les graphes sans croisement. Plus précisément, le groupe cyclique agit sur ces graphes naturellement par rotation et nous montrons que la structure d'orbite de cette action est codée par certains polynômes. Nos résultats confirment deux conjectures de Alan Guo.