Clemens Bruschek ; Hussein Mourtada ; Jan Schepers - Arc Spaces and Rogers-Ramanujan Identities

dmtcs:2904 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2904
Arc Spaces and Rogers-Ramanujan Identities

Authors: Clemens Bruschek 1; Hussein Mourtada ORCID-iD2; Jan Schepers 3

  • 1 University of Vienna [Vienna]
  • 2 Laboratoire de Mathématiques de Versailles
  • 3 Catholic University of Leuven - Katholieke Universiteit Leuven

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 Hilbert-Poincaré series of the arc space over a point of the base variety. In the case of the double point this is precisely the generating series for the integer partitions without equal or consecutive parts.


Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: 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]
Funding:
    Source : OpenAIRE Graph
  • Solving Algebraic Equations II; Funder: Austrian Science Fund (FWF); Code: P 21461
  • Approximation Theorems in Algebra and CR Geometry; Funder: Austrian Science Fund (FWF); Code: I 382

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV 0908.1777
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.0908.1777
  • 10.48550/arxiv.0908.1777
  • 0908.1777
Finite Groebner bases in infinite dimensional polynomial rings and applications

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