The First Positive Rank and Crank Moments for Overpartitions

George Andrews; Song Heng Chan; Byungchan Kim; Robert Osburn

doi:10.1007/s00026-016-0306-0

The First Positive Rank and Crank Moments for Overpartitions

George Andrews, Song Heng Chan, Byungchan Kim, Robert Osburn

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a strict inequality also holds for the first rank and crank moments of overpartitions and consider a new combinatorial interpretation in this setting.

Original language	English
Pages (from-to)	193-207
Number of pages	15
Journal	Annals of Combinatorics
Volume	20
Issue number	2
DOIs	https://doi.org/10.1007/s00026-016-0306-0
State	Published - 1 Jun 2016

Keywords

cranks
overpartitions
positive moments
positivity
ranks

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10.1007/s00026-016-0306-0

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title = "The First Positive Rank and Crank Moments for Overpartitions",

abstract = "In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a strict inequality also holds for the first rank and crank moments of overpartitions and consider a new combinatorial interpretation in this setting.",

keywords = "cranks, overpartitions, positive moments, positivity, ranks",

author = "George Andrews and Chan, \{Song Heng\} and Byungchan Kim and Robert Osburn",

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AU - Chan, Song Heng

AU - Kim, Byungchan

AU - Osburn, Robert

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AB - In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a strict inequality also holds for the first rank and crank moments of overpartitions and consider a new combinatorial interpretation in this setting.

KW - cranks

KW - overpartitions

KW - positive moments

KW - positivity

KW - ranks

UR - https://www.scopus.com/pages/publications/84971011068

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DO - 10.1007/s00026-016-0306-0

M3 - Article

AN - SCOPUS:84971011068

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EP - 207

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 2

ER -

The First Positive Rank and Crank Moments for Overpartitions

Abstract

Keywords

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