Overpartitions

2003/07/08 by Sylvie Corteel, Jeremy Lovejoy · 5 citations
Mathematics · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics

paper · pdf · doi:10.1090/s0002-9947-03-03328-2

Abstract

We discuss a generalization of partitions, called overpartitions, which have proven useful in several combinatorial studies of basic hypergeometric series. After showing how a number of finite products occurring in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding="application/x-tex">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -series have natural interpretations in terms of overpartitions, we present an introduction to their rich structure as revealed by <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding="application/x-tex">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -series identities.

Cited by

• On a two-color partition series and its companions
• The First Positive Rank and Crank Moments for Overpartitions
• Truncated theta series from the Bailey lattice
• Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang-Xie-Zhang. [europepmc]
• Log-convexity and the overpartition function. [europepmc]

Related

• Overpartition pairs and two classes of basic hypergeometric series
• Overpartitions with parts separated by parity
• The combinatorics of identities involving overpartitions with distinct parts
• Combinatorial identities and hypergeometric series
• "Overpartitionized" Rogers--Ramanujan type identities