4 citations · 9 across the 18 of their papers we have counts for
20 papers
Proofs for Andrews' Conjectures 5 and 6 on
Mohamed El Bachraoui
Folsom, Males, Rolen, and Storzer recently proved Andrews' Conjecture~4 for the coefficients of \[ v_1(q)=\sum_{n\ge 0}\frac{q^{n(n+1)/2}}{(-q^2;q^2)_n}=\sum_{n\ge 0}V_1(n)q^n. \]…
On congruence conjectures of Andrews and Bachraoui
Koustav Banerjee, Kathrin Bringmann, Mohamed El Bachraoui
Andrews and the third author recently studied congruences for certain restricted two-color partitions. They made two conjectures for Ramanujan-type congruences and a vanishing iden…
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…
Congruences for two-color partitions with odd smallest part
George E. Andrews, Mohamed El Bachraoui
For a fixed positive integer , let denote the number of two-color partitions of with odd smallest part and restrictions on even parts, and let be its gener…