Special Cases of the Parking Functions Conjecture and Upper-Triangular Matrices

• Main Author: Levande, Paul
• Other Authors: Department of Mathematics Philadelphia, University of Pennsylvania Philadelphia, Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2011
• Subjects: parking function; Hilbert series; diagonal harmonics; [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-01215036; https://hal.inria.fr/hal-01215036/document; https://hal.inria.fr/hal-01215036/file/dmAO0156.pdf

International audience We examine the $q=1$ and $t=0$ special cases of the parking functions conjecture. The parking functions conjecture states that the Hilbert series for the space of diagonal harmonics is equal to the bivariate generating function of $area$ and $dinv$ over the set of parking func...