Generalized higher order spt-functions

Atul Dixit, Ae Ja Yee

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)191-212
Number of pages22
JournalRamanujan Journal
Issue number1-2
StatePublished - Jun 2013

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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