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 ; Hussein Mourtada ORCID-iD; Jan Schepers

    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]
    Fundings :
      Source : OpenAIRE Research 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

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