On the asymptotic behavior of unimodal rank generating functions

Kathrin Bringmann; Byungchan Kim

doi:10.1016/j.jmaa.2015.10.057

On the asymptotic behavior of unimodal rank generating functions

Kathrin Bringmann, Byungchan Kim

School of Natural Sciences

University of Cologne

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

5 Scopus citations

Abstract

In a recent paper, J. Lovejoy and the second author conjectured that ranks for four types of unimodal like sequences satisfy certain inequalities. In this paper, we prove these conjectures asymptotically. For this, we use Wright's Circle Method and analyze the asymptotic behavior of certain general partial theta functions.

Original language	English
Pages (from-to)	627-645
Number of pages	19
Journal	Journal of Mathematical Analysis and Applications
Volume	435
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2015.10.057
State	Published - 1 Mar 2016

Keywords

Asymptotic methods
Circle Method
Partial theta functions
Unimodal ranks
Unimodal sequences

Access to Document

10.1016/j.jmaa.2015.10.057

Cite this

@article{e7c02d0a256748f0802812172a741640,

title = "On the asymptotic behavior of unimodal rank generating functions",

abstract = "In a recent paper, J. Lovejoy and the second author conjectured that ranks for four types of unimodal like sequences satisfy certain inequalities. In this paper, we prove these conjectures asymptotically. For this, we use Wright's Circle Method and analyze the asymptotic behavior of certain general partial theta functions.",

keywords = "Asymptotic methods, Circle Method, Partial theta functions, Unimodal ranks, Unimodal sequences",

author = "Kathrin Bringmann and Byungchan Kim",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2016",

month = mar,

day = "1",

doi = "10.1016/j.jmaa.2015.10.057",

language = "English",

volume = "435",

pages = "627--645",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

number = "1",

}

TY - JOUR

T1 - On the asymptotic behavior of unimodal rank generating functions

AU - Bringmann, Kathrin

AU - Kim, Byungchan

PY - 2016/3/1

Y1 - 2016/3/1

N2 - In a recent paper, J. Lovejoy and the second author conjectured that ranks for four types of unimodal like sequences satisfy certain inequalities. In this paper, we prove these conjectures asymptotically. For this, we use Wright's Circle Method and analyze the asymptotic behavior of certain general partial theta functions.

AB - In a recent paper, J. Lovejoy and the second author conjectured that ranks for four types of unimodal like sequences satisfy certain inequalities. In this paper, we prove these conjectures asymptotically. For this, we use Wright's Circle Method and analyze the asymptotic behavior of certain general partial theta functions.

KW - Asymptotic methods

KW - Circle Method

KW - Partial theta functions

KW - Unimodal ranks

KW - Unimodal sequences

UR - http://www.scopus.com/inward/record.url?scp=84960839703&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2015.10.057

DO - 10.1016/j.jmaa.2015.10.057

M3 - Article

AN - SCOPUS:84960839703

SN - 0022-247X

VL - 435

SP - 627

EP - 645

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

On the asymptotic behavior of unimodal rank generating functions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this