13 papers
The asymptotic behavior of the rectangle partition function
Krystian Gajdzica, Maciej Zakarczemny
Let denote the number of partitions of a rectangle into integer-sided rectangular blocks, where two partitions are indistinguishable if they consist of the sam…
A note on the partition function of a rectangle
Krystian Gajdzica, Maciej Zakarczemny
We investigate the asymptotic behavior of the rectangle partition functions and . The function counts partitions of the square into rectangula…
Submultiplicative Polynomials in Combinatorics
Krystian Gajdzica, Bernhard Heim, Markus Neuhauser +1
For normalized sequences we consider recursively defined polynomials . In this paper we study their submultiplicative property, viewe…
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…
Log-Concavity and Log-Convexity of Restricted Infinite Products
Krystian Gajdzica, Bernhard Heim, Markus Neuhauser
In this paper we provide a classification on the sign distribution of , where \begin{equation*} \sum_{n =0}…
On the Bessenrodt-Ono type inequality for a wide class of -partition functions
Krystian Gajdzica
The -partition function enumerates those partitions of whose parts belong to a fixed (finite or infinite) set of positive integers. On the other hand, the exten…