2 citations · 4 across the 11 of their papers we have counts for
12 papers
A -microscope for mock-theta denominator patterns
Mohamed El Bachraoui
We give a systematic creative-microscoping treatment of truncated basic hypergeometric sums attached to three classical third-order mock theta denominator patterns, represented by…
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…
Solutions for Hecke Sum Questions of Banerjee and Bringmann
George E. Andrews, Mohamed El Bachraoui
We previously conjectured a Hecke-type identity for a series arising from two-color partitions. Banerjee and Bringmann proved the conjecture using modular methods and asked for a d…
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…
A note on simple games with two equivalence classes of players
Sascha Kurz, Dani Samaniego
Many real-world voting systems consist of voters that occur in just two different types. Indeed, each voting system with a {\lq\lq}House{\rq\rq} and a {\lq\lq}Senat{\rq\rq} is of t…
Short proofs for -Raabe formula and integrals for Jacobi theta functions
Mohamed El Bachraoui
We shall answer a question of Mező on the -analogue of the Raabe's integral formula for and we shall evaluate an integral involving the first theta function. Moreover, w…
On finite sums involving
Mohamed El Bachraoui
We use an elementary argument to prove some finite sums involving expressions of the forms and along with inductive formulas for some sequences.
A gamma function in two variables
Mohamed El Bachraoui
We introduce a gamma function $\Ga(x,z)$ in two complex variables which extends the classical gamma function $\Ga(z)$ in the sense that $\lim_{x\to 1}\Ga(x,z)=\Ga(z)$. We will show…
On representations of positive integers by , , and
Mohamed El Bachraoui
We use sums of Liouville type to count the number of ways a positive integer can be represented by the forms , , and $\…
Elementary formulas for integer partitions
Mohamed El Bachraoui
In this note we will give various exact formulas for functions on integer partitions including the functions and of the number of partitions of and the number o…
Combinatorial Identities Via Phi Functions and Relatively Prime Subsets
Mohamed El Bachraoui
Let be a positive integer and let be nonempty finite set of positive integers. We say that is relatively prime if and that is relatively prime to i…
Combinatorial Identities Involving Mertens Function Through Relatively Prime Subsets
Mohamed El Bachraoui
In this note we give some identities which involve the Mertens function M(n). Our proofs are combinatorial with relatively prime subsets as a main tool.