Krystian Gajdzica

activity

20212026

collaborators

13 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.CO2026

Submultiplicative Polynomials in Combinatorics

Krystian Gajdzica, Bernhard Heim, Markus Neuhauser +1

For normalized sequences $(g (n))_{n \in N}$ we consider recursively defined polynomials $P_{n}^{g} (x)$ . In this paper we study their submultiplicative property, viewe…

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.CO2025

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 $Δ_{E, ℓ} (n) := p_{E, ℓ} (n)^{2} - p_{E, ℓ} (n - 1) p_{E, ℓ} (n + 1)$ , where \begin{equation*} \sum_{n =0}…

math.CO2024

On the Bessenrodt-Ono type inequality for a wide class of $A$ -partition functions

Krystian Gajdzica

The $A$ -partition function $p_{A} (n)$ enumerates those partitions of $n$ whose parts belong to a fixed (finite or infinite) set $A$ of positive integers. On the other hand, the exten…

math.NT2023

On general approach to Bessenrodt-Ono type inequalities and log-concavity property

Krystian Gajdzica, Piotr Miska, Maciej Ulas

In recent literature concerning integer partitions one can find many results related to both the Bessenrodt-Ono type inequalities and log-concavity property. In this note we offer…

math.CO2023

The Turán and Laguerre inequalities for quasi-polynomial-like functions

Krystian Gajdzica

This paper deals with both the higher order Turán inequalities and the Laguerre inequalities for quasi-polynomial-like functions -- that are expressions of the form $f(n)=c_l(n)n^l…

math.CO2023

Polynomization of the Bessenrodt-Ono type inequalities for A-partition functions

Krystian Gajdzica, Bernhard Heim, Markus Neuhauser

For an arbitrary set or multiset $A$ of positive integers, we associate the $A$ -partition function $p_{A} (n)$ (that is the number of partitions of $n$ whose parts belong to $A$ ). We…

math.CO2023

Restricted partition functions and the $r$ -log-concavity of quasi-polynomial-like functions

Krystian Gajdzica

Let $A = (a_{i})_{i = 1}^{\infty}$ be a weakly increasing sequence of positive integers and let $k$ be a fixed positive integer. For an arbitrary integer $n$ , the rest…

math.CO2022

Log-concavity of the restricted partition function $p_{A} (n, k)$ and the new Bessenrodt-Ono type inequality

Krystian Gajdzica

Let $A = (a_{i})_{i = 1}^{\infty}$ be a non-decreasing sequence of positive integers and let $k \in N_{+}$ be fixed. The function $p_{A} (n, k)$ counts the number of p…

math.NT2021

Discriminants of special quadrinomials

Krystian Gajdzica

Finding an effective formula for describing a discriminant of a quadrinomial (a formula which can be easily computed for high values of degrees of quadrinomials) is a difficult pro…

math.NT2021

A note on the restricted partition function $p_{A} (n, k)$

Krystian Gajdzica

Let $A = (a_{n})_{n \in N_{+}}$ be a sequence of positive integers. Let $p_{A} (n, k)$ denote the number of multi-color partitions of $n$ into parts in $\{a_1,\ldo…

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

A note on the partition function of a rectangle

Submultiplicative Polynomials in Combinatorics

Rectangle partitions generalizing integer partitions

Log-Concavity and Log-Convexity of Restricted Infinite Products

On the Bessenrodt-Ono type inequality for a wide class of A-partition functions

On general approach to Bessenrodt-Ono type inequalities and log-concavity property

The Turán and Laguerre inequalities for quasi-polynomial-like functions

Polynomization of the Bessenrodt-Ono type inequalities for A-partition functions

Restricted partition functions and the r-log-concavity of quasi-polynomial-like functions

Log-concavity of the restricted partition function pA​(n,k) and the new Bessenrodt-Ono type inequality

Discriminants of special quadrinomials

A note on the restricted partition function pA​(n,k)

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

On the Bessenrodt-Ono type inequality for a wide class of $A$ -partition functions

Restricted partition functions and the $r$ -log-concavity of quasi-polynomial-like functions

Log-concavity of the restricted partition function $p_{A} (n, k)$ and the new Bessenrodt-Ono type inequality

A note on the restricted partition function $p_{A} (n, k)$