Maciej Zakarczemny

activity

20242026

collaborators

5 papers

math.CO2026

The asymptotic behavior of the rectangle partition function $p (m, n)$

Krystian Gajdzica, Maciej Zakarczemny

Let $p (m, n)$ denote the number of partitions of a rectangle $m \times n$ into integer-sided rectangular blocks, where two partitions are indistinguishable if they consist of the sam…

math.CO2026

A note on the partition function of a rectangle

Krystian Gajdzica, Maciej Zakarczemny

We investigate the asymptotic behavior of the rectangle partition functions $p (n, n)$ and $p (3, n)$ . The function $p (n, n)$ counts partitions of the square $n \times n$ into rectangula…

math.NT2026

On the Diophantine Equation Involving Elementary Symmetric Polynomials and the Decomposition of Unity

Sándor Z. Kiss, Csaba Sándor, Maciej Zakarczemny

We consider the equality of the values of the $n$ th and $k$ th elementary symmetric polynomials of $n$ not necessarily distinct positive integers. For $k < n$ , we prove that this eq…

math.CO2025

Rectangle partitions generalizing integer partitions

Krystian Gajdzica, Robin Visser, Maciej Zakarczemny

In this paper, we introduce a natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a rectangle into rectangul…

math.NT2024

Equal Sum and Product Problem III

Csaba Sándor, Maciej Zakarczemny

Denote by $N (n)$ the number of integer solutions $(x_{1}, x_{2}, \dots, x_{n})$ of the equation $x_{1} + x_{2} + \dots + x_{n} = x_{1} x_{2} \cdot \dots \cdot x_{n}$ such that $x_1\ge x_2\ge\ldots\ge x_n\ge…