Arc Spaces and Rogers-Ramanujan Identities
By C. Bruschek, H. Mourtada, Jan Schepers. 2011
57 citations recorded by the source corpus.
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-Poincare 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.
View Paper: https://www.semanticscholar.org/paper/b4fa4fbb2b363a57a6bcdd2f325494f92e7195d0
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Citations in the corpus
- A framework of Rogers–Ramanujan identities and their arithmetic properties (2014, background): “y. ROGERS–RAMANUJAN IDENTITIES AND THEIR ARITHMETIC PROPERTIES 3 first recognized by MacMahon and Schur as identities for integer partitions [49, 57]. They have since been linked to algebraic geometry [18, 29], K-theory [23], conformal field theory [10, 36], group theory [25], Kac–Moody and double affin”