3 papers
math.CO2017
Some Elementary Partition Inequalities and Their Implications
Alexander Berkovich, Ali K. Uncu
We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequ…
math.CO2016
Weighted Rogers-Ramanujan Partitions and Dyson Crank
Ali Kemal Uncu
In this paper we refine a weighted partition identity of Alladi. We write explicit formulas of generating functions for the number of partitions grouped with respect to a partition…
math.CO2015
A New Companion to Capparelli's Identities
Alexander Berkovich, Ali Kemal Uncu
We discuss a new companion to Capparelli's identities. Capparelli's identities for m=1,2 state that the number of partitions of into distinct parts not congruent to m, -m modul…