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TitleArc spaces and the Rogers-Ramanujan identities.
Author(s) Clemens Bruschek, Svante Janson, Hussein Mourtada
TypeArticle in Journal
AbstractArc 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.
KeywordsArc spaces, Hilbert–Poincaré series, Rogers–Ramanujan identities, Gröbner bases
ISSN1382-4090; 1572-9303/e
URL http://link.springer.com/article/10.1007%2Fs11139-012-9401-y
LanguageEnglish
JournalRamanujan J.
Volume30
Number1
Pages9--38
PublisherSpringer US, New York, NY
Year2013
Edition0
Translation No
Refereed No
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