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Arc Spaces and Rogers-Ramanujan Identities

Abstract : 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.
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Clemens Bruschek, Hussein Mourtada, Jan Schepers. Arc Spaces and Rogers-Ramanujan Identities. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.211-220. ⟨hal-01215083⟩



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