George E. Andrews

activity

20242026

most citedCongruences for two-color partitions with odd smallest part

1 citations · 1 across the 11 of their papers we have counts for

collaborators

11 papers

math.NT2026

A surprising generalization of the Möbius function

George E. Andrews, Louis H. Kauffman, Divyamaan Sahoo

We introduce a broad generalization of a recursive formula for the Möbius function $μ (n) = 1 - n - \sum_{d = 2}^{n - 1} μ (d) [\frac{n}{d}]$ due to George Spencer-Brown. By replaci…

math.CO2026

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_…

math.NT2026

Weighted partitions with interval restrictions: exact formulas and a bivariate master identity

George E. Andrews, Mohamed El Bachraoui, Aritram Dhar +2

Let $a_{2}^{''} (n)$ and $b_{2}^{''} (n)$ be the signed partition functions introduced by Andrews and El Bachraoui for interval-restricted partitions whose parts greater than $1$ are controlle…

math.NT2026

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…

math.NT2025

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…

math.NT2025

Certain positive $q$ -series and inequalities for two-color partitions

George E. Andrews, Mohamed El Bachraoui

We consider some $q$ -series which depend on a pair of positive integers $(k, m)$ . While positivity of these series holds for the first few values of $(k, m)$ , the situation is quite…

math.NT2025

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 $q$ -double series and deduce that their co…

math.CO2025

On a formula of the $q$ -series $_{2 k + 4} ϕ_{2 k + 3}$ and its applications

George E. Andrews, Mohamed El Bachraoui

In this paper we apply a formula of the very-well poised $_{2 k + 4} ϕ_{2 k + 3}$ to write a $k$ -tuple sum of $q$ -series as a linear combination of terms wherein each term is a product of…

math.NT2024

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…

math.CO2024

Identities involving partitions with distinct even parts and $4$ -regular partitions

George E. Andrews, Mohamed El Bachraoui

It is well known that the number of partitions into distinct even parts equals the number of $4$ -regular partitions. In this paper we prove identities relating certain restricted p…

math.NT2024★ 1 cited

Congruences for two-color partitions with odd smallest part

George E. Andrews, Mohamed El Bachraoui

For a fixed positive integer $k$ , let $C (k, n)$ denote the number of two-color partitions of $n$ with odd smallest part and restrictions on even parts, and let $C_{k} (q)$ be its gener…

A surprising generalization of the Möbius function

On a two-color partition series and its companions

Weighted partitions with interval restrictions: exact formulas and a bivariate master identity

Solutions for Hecke Sum Questions of Banerjee and Bringmann

Two-color partitions with evens in one color

Certain positive q-series and inequalities for two-color partitions

Positive Weighted Partitions Generated by Double Series

On a formula of the q-series 2k+4​ϕ2k+3​ and its applications

Legendre theorems for certain overpartitions and overpartition pairs

Identities involving partitions with distinct even parts and 4-regular partitions

Congruences for two-color partitions with odd smallest part

Certain positive $q$ -series and inequalities for two-color partitions

On a formula of the $q$ -series $_{2 k + 4} ϕ_{2 k + 3}$ and its applications

Identities involving partitions with distinct even parts and $4$ -regular partitions