George E. Andrews · wovepaper

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20242026

most citedCongruences for two-color partitions with odd smallest part

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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…

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…

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…

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…

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…

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.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…