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

Mathematics

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 (US)
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 - Jun 1 2016

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

Access to Document

10.1007/s00026-016-0306-0

Cite this

@article{7bc52af8e4b8414ab9b4f0d4dccedeb6,

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.",

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

note = "Publisher Copyright: {\textcopyright} 2016, Springer International Publishing.",

year = "2016",

month = jun,

day = "1",

doi = "10.1007/s00026-016-0306-0",

language = "English (US)",

volume = "20",

pages = "193--207",

journal = "Annals of Combinatorics",

issn = "0218-0006",

publisher = "Springer International Publishing",

number = "2",

}

TY - JOUR

T1 - The First Positive Rank and Crank Moments for Overpartitions

AU - Andrews, George

AU - Chan, Song Heng

AU - Kim, Byungchan

AU - Osburn, Robert

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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.

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.

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

UR - https://www.scopus.com/pages/publications/84971011068#tab=citedBy

U2 - 10.1007/s00026-016-0306-0

DO - 10.1007/s00026-016-0306-0

M3 - Article

AN - SCOPUS:84971011068

SN - 0218-0006

VL - 20

SP - 193

EP - 207

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 2

ER -

The First Positive Rank and Crank Moments for Overpartitions

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this