![[Abstract]](http://www.math.ufl.edu/~frank/icons/scroll.gif)
George E. Andrews, Frank G. Garvan and Jie Liang;
Combinatorial interpretations of congruences for the spt-function,
Ramanujan J., to appear.
Abstract:
Let spt(n) denote the total number of appearances
of the smallest parts in all the partitions of n. In 1988, the
second author gave new combinatorial interpretations of
Ramanujan's partition congruences mod 5, 7 and 11 in terms of
a crank for weighted vector partitions. In 2008, the first
author found Ramanujan- type congruences for the spt-function
mod 5, 7 and 13. We give new combinatorial interpretations of
the spt-congruences mod 5 and 7. These are in terms of the
same crank but for a restricted set of vector partitions. The
proof depends on relating the spt-crank with the crank of
vector partitions and the Dyson rank of ordinary partitions.
We derive a number of identities for spt-crank modulo 5 and
7. We prove the surprising result that all the spt-crank
coefficients are nonnegative.
The url of this page is http://qseries.org/fgarvan/abstracts/spt-crank.html.
Created by
F.G. Garvan
(fgarvan@ufl.edu) on
Wednesday, October 12, 2011.
Last update made Tue Jan 10 09:29:12 EST 2012.
fgarvan@ufl.edu
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