Maciej Zakarczemny

activity

20242026

collaborators

Showing 2026Show all

3 papers · 1 filter

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…

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

A note on the partition function of a rectangle

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

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