5 papers
Certain positive -series and inequalities for two-color partitions
George E. Andrews, Mohamed El Bachraoui
We consider some -series which depend on a pair of positive integers . While positivity of these series holds for the first few values of , the situation is quite…
Positive Weighted Partitions Generated by Double Series
George E. Andrews, Mohamed El Bachraoui
We investigate some weighted integer partitions whose generating functions are double-series. We will establish closed formulas for these -double series and deduce that their co…
On a formula of the -series and its applications
George E. Andrews, Mohamed El Bachraoui
In this paper we apply a formula of the very-well poised to write a -tuple sum of -series as a linear combination of terms wherein each term is a product of…
Legendre theorems for certain overpartitions and overpartition pairs
George E. Andrews, Mohamed El Bachraoui
Motivated by two Legendre-type formulas for overpartitions, we derive a variety of their companions as Legendre theorems for overpartition pairs. This leads to equalities of subcla…
Identities involving partitions with distinct even parts and -regular partitions
George E. Andrews, Mohamed El Bachraoui
It is well known that the number of partitions into distinct even parts equals the number of -regular partitions. In this paper we prove identities relating certain restricted p…