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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…
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…