Generalized higher order spt-functions

Atul Dixit; Ae Ja Yee

doi:10.1007/s11139-012-9434-2

Generalized higher order spt-functions

Atul Dixit, Ae Ja Yee

Mathematics

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

7 Scopus citations

Abstract

We give a new generalization of the spt-function of G. E. Andrews, namely Spt_j(n), and give its combinatorial interpretation in terms of successive lower-Durfee squares. We then generalize the higher order spt-function spt_k(n), due to F. G. Garvan, to _jspt_k(n), thus providing a two-fold generalization of spt_n, and give its combinatorial interpretation. Lastly, we show how the positivity of _jspt_k(n) can be used to generalize Garvan's inequality between rank and crank moments to the moments of j-rank and (j+1)-rank.

Original language	English (US)
Pages (from-to)	191-212
Number of pages	22
Journal	Ramanujan Journal
Volume	31
Issue number	1-2
DOIs	https://doi.org/10.1007/s11139-012-9434-2
State	Published - Jun 2013

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

10.1007/s11139-012-9434-2

Cite this

@article{a326424a6bfe4626a3940953f45ccac8,

title = "Generalized higher order spt-functions",

abstract = "We give a new generalization of the spt-function of G. E. Andrews, namely Sptj(n), and give its combinatorial interpretation in terms of successive lower-Durfee squares. We then generalize the higher order spt-function sptk(n), due to F. G. Garvan, to jsptk(n), thus providing a two-fold generalization of sptn, and give its combinatorial interpretation. Lastly, we show how the positivity of jsptk(n) can be used to generalize Garvan's inequality between rank and crank moments to the moments of j-rank and (j+1)-rank.",

author = "Atul Dixit and Yee, {Ae Ja}",

note = "Funding Information: The second author was partially supported by National Security Agency Grant H98230-10-1-0205 and by the Australian Research Council.",

year = "2013",

month = jun,

doi = "10.1007/s11139-012-9434-2",

language = "English (US)",

volume = "31",

pages = "191--212",

journal = "Ramanujan Journal",

issn = "1382-4090",

publisher = "Springer Netherlands",

number = "1-2",

}

TY - JOUR

T1 - Generalized higher order spt-functions

AU - Dixit, Atul

AU - Yee, Ae Ja

N1 - Funding Information: The second author was partially supported by National Security Agency Grant H98230-10-1-0205 and by the Australian Research Council.

PY - 2013/6

Y1 - 2013/6

N2 - We give a new generalization of the spt-function of G. E. Andrews, namely Sptj(n), and give its combinatorial interpretation in terms of successive lower-Durfee squares. We then generalize the higher order spt-function sptk(n), due to F. G. Garvan, to jsptk(n), thus providing a two-fold generalization of sptn, and give its combinatorial interpretation. Lastly, we show how the positivity of jsptk(n) can be used to generalize Garvan's inequality between rank and crank moments to the moments of j-rank and (j+1)-rank.

AB - We give a new generalization of the spt-function of G. E. Andrews, namely Sptj(n), and give its combinatorial interpretation in terms of successive lower-Durfee squares. We then generalize the higher order spt-function sptk(n), due to F. G. Garvan, to jsptk(n), thus providing a two-fold generalization of sptn, and give its combinatorial interpretation. Lastly, we show how the positivity of jsptk(n) can be used to generalize Garvan's inequality between rank and crank moments to the moments of j-rank and (j+1)-rank.

UR - http://www.scopus.com/inward/record.url?scp=84876951661&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876951661&partnerID=8YFLogxK

U2 - 10.1007/s11139-012-9434-2

DO - 10.1007/s11139-012-9434-2

M3 - Article

AN - SCOPUS:84876951661

SN - 1382-4090

VL - 31

SP - 191

EP - 212

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 1-2

ER -

Generalized higher order spt-functions

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this