Hyperplane Arrangements and Diagonal Harmonics

• Main Author: Armstrong, Drew
• Other Authors: Department of Mathematics Miami, University of Miami Coral Gables, Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2011
• Subjects: Shi arrangement; Ish arrangement; affine permutations; diagonal harmonics; Catalan numbers; nabla operator; parking functions; [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]; [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]; Haglund; Iceland
• Online Access: https://hal.inria.fr/hal-01215088; https://hal.inria.fr/hal-01215088/document; https://hal.inria.fr/hal-01215088/file/dmAO0105.pdf

International audience In 2003, Haglund's bounce statistic gave the first combinatorial interpretation of the q,t-Catalan numbers and the Hilbert series of diagonal harmonics. In this paper we propose a new combinatorial interpretation in terms of the affine Weyl group of type A. In particular,...