2 citations · 2 across the 5 of their papers we have counts for
18 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…
Goellnitz-Gordon partitions with weights and parity conditions
Krishnaswami Alladi, Alexander Berkovich
A Goellnitz-Gordon partition is one in which the parts differ by at least 2, and where the inequality is strict if a part is even. Let Q_i(n) denote the number of partitions of n i…
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…
A limiting form of the q-Dixon_4ϕ_3 summation and related partition identities
Krishnaswami Alladi, Alexander Berkovich
By considering a limiting form of the q-Dixon_4ϕ_3 summation, we prove a weighted partition theorem involving odd parts differing by >= 4. A two parameter refinement of this theore…
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…