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math.CO2002
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…
math.CO2002
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…
math.CO2002
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…