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Two-color partitions with evens in one color
George E. Andrews, Mohamed El Bachraoui
We consider sequences counting integer partitions in two colors (red and blue) in which the even parts occur only in blue color. We focus on subsequences defined by constraints on…
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…