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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory