10 citations · 12 across the 19 of their papers we have counts for
26 papers
A Positive Proportion of the Reduced D'Arcais Polynomials is not Hurwitz
Steven Charlton, Bernhard Heim, Markus Neuhauser +2
Heretofore, the second and third author conjectured that the D'Arcais polynomials, related to the coefficients of the powers of the Dedekind -function, are Hurwitz polynomials e…
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…
Dominant Zeros of Nekrasov--Okounkov Polynomials
Bernhard Heim, Markus Neuhauser, with an appendix by Ken Ono
We give an exact finite-dimensional Perron--Frobenius realization of the dominant zero of the Nekrasov--Okounkov polynomials $\nop _n(z)$. For a normalized positive sequence $h=(h(…
Polynomization of Sun's Conjecture
Bernhard Heim und Markus Neuhauser
Let denote the number of partitions of a natural number . As , the th root of tends to , which is related to the Cauchy--Hadamard test for pow…
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 Non-vanishing of the D'Arcais Polynomials
Bernhard Heim, Markus Neuhauser
In this paper we invest in the non-vanishing of the Fourier coefficients of powers of the Dedekind eta function. This is reflected in non-vanishing properties of the D'Arcais polyn…
Bessenrodt--Ono inequalities for -tuples of pairwise commuting permutations
Abdelmalek Abdesselam, Bernhard Heim, Markus Neuhauser
Let denote the symmetric group. We consider \begin{equation*} N_{\ell}(n) := \frac{\left\vert Hom\left( \mathbb{Z}^{\ell},S_n\right) \right\vert}{n!} \end{equation*} which al…
Sequences with Inequalities
Bernhard Heim und Markus Neuhauser
We consider infinite sequences of positive numbers. The connection between log-concavity and the Bessenrodt--Ono inequality had been in the focus of several papers. This has applic…
Inequalities for -regular partitions
Bernhard Heim, Markus Neuhauser
We build upon the work by Bessenrodt and Ono, as well as Beckwith and Bessenrodt concerning the combined additive and multiplicative behavior of the -regular partition functions…
On a mod property of -tuples of pairwise commuting permutations
Abdelmalek Abdesselam, Bernhard Heim, Markus Neuhauser
Let denote the symmetric group of permutations acting on elements. We investigate the double sequence counting the number of tuples of elements o…
Polynomization of the Bessenrodt-Ono type inequalities for A-partition functions
Krystian Gajdzica, Bernhard Heim, Markus Neuhauser
For an arbitrary set or multiset of positive integers, we associate the -partition function (that is the number of partitions of whose parts belong to ). We…
Zeros Transfer For Recursively defined Polynomials
Bernhard Heim, Markus Neuhauser, Robert Troeger
The zeros of D'Arcais polynomials, also known as Nekrasov--Okounkov polynomials, dictate the vanishing of the Fourier coefficients of powers of the Dedekind functions. These polyno…
Log-Concavity of Infinite Product and Infinite Sum Generating Functions
Bernhard Heim, Markus Neuhauser
We expand on the remark by Andrews on the importance of infinite sums and products in combinatorics. Let be the double sequences $σ_d(n)= \sum_{\ell…
Asymptotic Normality of the Coefficients of the Morgan-Voyce Polynomials
Moussa Benoumhani, Bernhard Heim, Markus Neuhauser
We study arithmetic and asymptotic properties of polynomials provided by with initial value . The coefficients satisfy a central…
Turán inequalities from Chebyshev to Laguerre polynomials
Bernhard Heim, Markus Neuhauser, Robert Troeger
Let and be real-valued arithmetic functions, positive and normalized. Specific choices within the following general scheme of recursively defined polynomials \begin{equatio…
Inequalities for Plane Partitions
Bernhard Heim, Markus Neuhauser, Robert Tröger
Inequalities are important features in the context of sequences of numbers and polynomials. The Bessenrodt--Ono inequality for partition numbers and Nekrasov--Okounkov polynomials…
Proof of the Bessenrodt--Ono inequality by Induction
Bernhard Heim, Markus Neuhauseer
In 2016 Bessenrodt--Ono discovered an inequality addressing additive and multiplicative properties of the partition function. Generalization by several authors have been given; on…
Asymptotic Distribution of the Zeros of recursively defined Non-Orthogonal Polynomials
Bernhard Heim, Markus Neuhauser
We study the zero distribution of non-orthogonal polynomials attached to : \begin{equation*} Q_n^g(x)= x \sum_{k=1}^n g(k) \, Q_{n-k}^g(x), \quad Q_0^g(x):=1. \end{e…
Asymptotic expansion of Fourier coefficients of reciprocals of Eisenstein series
Bernhard Heim, Markus Neuhauser
In this paper we give a classification of the asymptotic expansion of the -expansion of reciprocals of Eisenstein series of weight for the modular group $\func{SL}_2(\…
On the growth and zeros of polynomials attached to arithmetic functions
Bernhard Heim, Markus Neuhauser
In this paper we investigate growth properties and the zero distribution of polynomials attached to arithmetic functions and , where is normalized, of moderate growth, a…
Polynomization of the Chern--Fu--Tang conjecture
Bernhard Heim, Markus Neuhauser
Bessenrodt and Ono's work on additive and multiplicative properties of the partition function and DeSalvo and Pak's paper on the log-concavity of the partition function have genera…
Formulas for coefficients of polynomials assigned to arithmetic functions
Bernhard Heim, Markus Neuhauser
We attach to normalized (non-vanishing) arithmetic functions and recursively defined polynomials. Let . Then \begin{equation} P_n^{g,h}(x) := \frac{x}{h(n)…
Horizontal and Vertical Log-Concavity
Bernhard Heim, Markus Neuhauser
Horizontal and vertical generating functions and recursion relations have been investigated by Comtet for triangular double sequences. In this paper we investigate the horizontal a…
Polynomization of the Bessenrodt-Ono inequality
Bernhard Heim, Markus Neuhauser, Robert Tröger
In this paper we investigate the generalization of the Bessenrodt--Ono inequality by following Gian-Carlo Rota's advice in studying problems in combinatorics and number theory in t…