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A Computer Proof of a Polynomial Identity Implying a Partition Theorem of Göllnitz

✍ Scribed by Alexander Berkovich; Axel Riese

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
117 KB
Volume
28
Category
Article
ISSN
0196-8858

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✦ Synopsis

In this paper we give a computer proof of a new polynomial identity, which extends a recent result of Alladi and the first author. In addition, we provide computer proofs for new finite analogs of Jacobi and Euler formulas. All computer proofs are done with the aid of the new computer algebra package qMultiSum developed by the second author. qMultiSum implements an algorithmic refinement of Wilf and Zeilberger's multi-q-extension of Sister Celine's technique utilizing additional ideas of Verbaeten and Wegschaider.  2002 Elsevier Science (USA)

1. G ÖLLNITZ'S PARTITION THEOREM AND RELATED

q-HYPERGEOMETRIC IDENTITIES In 1967, Göllnitz [6] proved the following deep partition theorem:

Theorem 1.1. Let A N denote the number of partitions of N in the form N = n 1 + n 2 + n 3 + • • •, such that no part is equal to 1 or 3, and n i -n i+1 ≥ 6 with strict inequality if n i ≡ 0 1 3 mod 6 .

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