Generalized higher order spt-functions

Atul Dixit, Ae Ja Yee

Research output: Contribution to journalArticlepeer-review

9 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 j spt k (n), thus providing a two-fold generalization of spt n , and give its combinatorial interpretation. Lastly, we show how the positivity of j spt 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 languageEnglish (US)
Pages (from-to)191-212
Number of pages22
JournalRamanujan Journal
Volume31
Issue number1-2
DOIs
StatePublished - Jan 1 2013

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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