Maciej Zakarczemny

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20242026

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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.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…

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

A note on the partition function of a rectangle

Rectangle partitions generalizing integer partitions

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