Geodesic
Arc Spaces and Rogers-Ramanujan Identities
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

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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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     author = {Bruschek, Clemens and Mourtada, Hussein and Schepers, Jan},
     title = {Arc {Spaces} and {Rogers-Ramanujan} {Identities}},
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Bruschek, Clemens; Mourtada, Hussein; Schepers, Jan. Arc Spaces and Rogers-Ramanujan Identities. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2904. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2904/

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