Bernhard Heim

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20242026

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4 papers · 1 filter

math.CO2024

Bessenrodt--Ono inequalities for $ℓ$ -tuples of pairwise commuting permutations

Abdelmalek Abdesselam, Bernhard Heim, Markus Neuhauser

Let $S_{n}$ 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…

math.CO2024

On a sign-change conjecture of Schlosser and Zhou

Kathrin Bringmann, Bernhard Heim, Ben Kane

In this paper, we investigate the signs changes of Fourier coefficients of infinite products of $q$ -series of Rogers--Ramanujan type. In particular, we prove a conjecture made by S…

math.CO2024

Inequalities for $k$ -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 $k$ -regular partition functions…

math.CO2024

On a mod $3$ property of $ℓ$ -tuples of pairwise commuting permutations

Abdelmalek Abdesselam, Bernhard Heim, Markus Neuhauser

Let $S_{n}$ denote the symmetric group of permutations acting on $n$ elements. We investigate the double sequence ${N_{ℓ} (n)}$ counting the number of $ℓ$ tuples of elements o…

Bessenrodt--Ono inequalities for ℓ-tuples of pairwise commuting permutations

On a sign-change conjecture of Schlosser and Zhou

Inequalities for k-regular partitions

On a mod 3 property of ℓ-tuples of pairwise commuting permutations

Bessenrodt--Ono inequalities for $ℓ$ -tuples of pairwise commuting permutations

Inequalities for $k$ -regular partitions

On a mod $3$ property of $ℓ$ -tuples of pairwise commuting permutations