9 papers
On a two-color partition series and its companions
George E. Andrews, Mohamed El Bachraoui
We study the two-color distinct-part series \(S_1(q)\), equivalently Andrews' generating function \(v_d(q)\) for strictly concave compositions, and its odd and even companions \(T_…
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…
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…
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…