A reciprocity approach to computing generating functions for permutations with no pattern matches

• Main Authors: Jones, Miles Eli, Remmel, Jeffrey
• Other Authors: Department of Mathematics Univ California San Diego (MATH - UC San Diego), University of California San Diego (UC San Diego), University of California (UC)-University of California (UC), Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2011
• Subjects: permutation; pattern match; descent; left to right minimum; symmetric polynomial; exponential generating function; [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]; [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]; Gauche; Iceland
• Online Access: https://inria.hal.science/hal-01215054; https://inria.hal.science/hal-01215054/document; https://inria.hal.science/hal-01215054/file/dmAO0149.pdf; https://doi.org/10.46298/dmtcs.2933

International audience In this paper, we develop a new method to compute generating functions of the form $NM_τ (t,x,y) = \sum\limits_{n ≥0} {\frac{t^n} {n!}}∑_{σ ∈\mathcal{lNM_{n}(τ )}} x^{LRMin(σ)} y^{1+des(σ )}$ where $τ$ is a permutation that starts with $1, \mathcal{NM_n}(τ )$ is the set of per...