2011/01/25 by Clemens Bruschek, Bruschek, Clemens, Hussein Mourtada +3 · 2 citations
Mathematics · #05A17 #11P84 #13P10 #14B05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1101.4950
openalex publication_date 2011/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.