Clemens Bruschek ; Hussein Mourtada ; Jan Schepers
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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)
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https://doi.org/10.46298/dmtcs.2904
Arc Spaces and Rogers-Ramanujan Identities
Authors: Clemens Bruschek 1; Hussein Mourtada 2; Jan Schepers 3
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Clemens Bruschek;Hussein Mourtada;Jan Schepers
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.