• Combinatorial proofs of an ide...

Result: Combinatorial proofs of an identity from Ramanujan's lost notebook and its variations

Title:
Combinatorial proofs of an identity from Ramanujan's lost notebook and its variations
Authors:
LEVANDE, Paul
Source:
Discrete mathematics. 310(17-18):2460-2467
Publisher Information:
Kidlington: Elsevier, 2010.
Publication Year:
2010
Physical Description:
print, 6 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Problèmes combinatoires classiques, Classical combinatorial problems, Algèbre, Algebra, Géométrie algébrique, Algebraic geometry, Analyse mathématique, Mathematical analysis, Analyse fonctionnelle, Functional analysis, Combinatoire, Combinatorics, Combinatoria, Dualité, Duality, Dualidad, Identité combinatoire, Combinatorial identity, Identidad combinatoria, Mathématiques discrètes, Discrete mathematics, Matemáticas discretas, Partition, Partición, Preuve, Proof, Prueba, Produit, Product, Producto, 05A19, 14H42, 46Kxx, Fonction partielle, Bijective proof, Partial theta function, Partition identity, Ramanujan's lost notebook
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia, PA 19104-6395, United States
ISSN:
0012-365X
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=23024485
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.23024485
Database:
PASCAL Archive

Further Information

We give two combinatorial proofs and partition-theoretic interpretations of an identity from Ramanujan's lost notebook. We prove a special case of the identity using the involution principle. We then extend this into a direct proof of the full identity using a generalization of the involution principle. We also show that the identity can be rewritten into a modified form that we prove bijectively. This fits the identity into Pak's duality of partition identities proven using the involution principle and partition identities proven bijectively. The original identity was first proven algebraically by Andrews as a consequence of an identity of Rogers' and combinatorially by Kim, while the modified form of the identity generalizes an identity recently found by Andrews and Warnaar related to the product of partial theta functions.