2 citations · 2 across the 4 of their papers we have counts for
5 papers
Dissecting the Stanley Partition Function
Alexander Berkovich, Frank G. Garvan
Let p(n) denote the number of unrestricted partitions of n. For i=0, 2, let p[i](n) denote the number of partitions pi of n such that O(pi) - O(pi') = i mod 4. Here O(pi) denotes t…
On the Andrews-Stanley Refinement of Ramanujan's Partition Congruence Modulo 5 and Generalizations
Alexander Berkovich, Frank G. Garvan
In a recent study of sign-balanced, labelled posets Stanley, introduced a new integral partition statistic srank(pi) = O(pi) - O(pi'), where O(pi) denotes the number of odd parts o…
On the Andrews-Stanley Refinement of Ramanujan's Partition Congruence Modulo 5
Alexander Berkovich, Frank G. Garvan
In a recent study of sign-balanced, labelled posets Stanley [13], introduced a new integral partition statistic srank(pi) = O(pi) - O(pi'), where O(pi) denotes the number of odd pa…
Relations between the ranks and cranks of partitions
A. O. L. Atkin, F. G. Garvan
New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functio…
Some Observations on Dyson's New Symmetries of Partitions
Alexander Berkovich, Frank G. Garvan
We utilize Dyson's concept of the adjoint of a partition to derive an infinite family of new polynomial analogues of Euler's Pentagonal Number Theorem. We streamline Dyson's biject…