10 papers
Weighted partitions with interval restrictions: exact formulas and a bivariate master identity
George E. Andrews, Mohamed El Bachraoui, Aritram Dhar +2
Let and be the signed partition functions introduced by Andrews and El Bachraoui for interval-restricted partitions whose parts greater than are controlle…
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…
Solutions for Hecke Sum Questions of Banerjee and Bringmann
George E. Andrews, Mohamed El Bachraoui
The present authors introduced a two-color partition series and conjectured a Hecke-type formula for the even part of . Banerjee and Bringmann proved…
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…
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…