7 papers
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…
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…
New polynomial analogues of Jacobi's triple product and Lebesgue's identities
Krishnaswami Alladi, Alexander Berkovich
In a recent paper by the authors, a bounded version of Goellnitz's (big) partition theorem was established. Here we show among other things how this theorem leads to nontrivial new…
New Weighted Rogers-Ramanujan Partition Theorems and their Implications
Krishnaswami Alladi, Alexander Berkovich
This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan p…
A double bounded key identity for Goellnitz's (big) partition theorem
K. Alladi, A. Berkovich
Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) the…
A Double Bounded Version of Schur's Partition Theorem
K. Alladi, A. Berkovich
Schur's partition theorem states that the number of partitions of n into distinct parts congruent 1, 2 (mod 3) equals the number of partitions of n into parts which differ by >= 3,…