Arc Spaces and Rogers-Ramanujan Identities

• Main Authors: Bruschek, Clemens, Mourtada, Hussein, Schepers, Jan
• Other Authors: University of Vienna Vienna, Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Catholic University of Leuven - Katholieke Universiteit Leuven (KU Leuven), Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2011
• Subjects: formal power series; Hilbert-Poincaré series; partitions; Rogers-Ramanujan Identities; arc spaces; infinite dimensional Gröbner basis; [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]; [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]; Double Point; Iceland
• Online Access: https://hal.inria.fr/hal-01215083; https://hal.inria.fr/hal-01215083/document; https://hal.inria.fr/hal-01215083/file/dmAO0120.pdf

International audience Arc spaces have been introduced in algebraic geometry as a tool to study singularities but they show strong connections with combinatorics as well. Exploiting these relations we obtain a new approach to the classical Rogers-Ramanujan Identities. The linking object is the Hilbe...