Cyclic sieving phenomenon in non-crossing connected graphs

• Main Author: Guo, Alan
• Other Authors: Department of Mathematics Durham, Duke University Durham, Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2011
• Subjects: non-crossing connected graphs; Lagrange inversion; cyclic sieving phenomenon; [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]; [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]; Lagrange; Iceland
• Online Access: https://hal.inria.fr/hal-01215104; https://hal.inria.fr/hal-01215104/document; https://hal.inria.fr/hal-01215104/file/dmAO0139.pdf

International audience A non-crossing connected graph is a connected graph on vertices arranged in a circle such that its edges do not cross. The count for such graphs can be made naturally into a q-binomial generating function. We prove that this generating function exhibits the cyclic sieving phenomenon, as conjectured by S.-P. Eu. Un graphe connexe dont les sommets sont disposés sur un cercle est sans croisement si ses arêtes ne se croisent pas. Nous démontrons une conjecture de S.-P. Eu affirmant que la fonction génératrice q-binomiale dénombrant de tels graphes exhibe le phénomène du crible cyclique.