R. Waldi

activity

20112024

most citedCounting numerical semigroups

5 citations · 8 across the 9 of their papers we have counts for

collaborators

9 papers

math.NT2024

On the order of magnitude of certain integer sequences

Michael Hellus, Anton Rechenauer, Rolf Waldi

Let $p$ be a prime number, and let $S$ be the numerical semigroup generated by the prime numbers not less than $p$ . We compare the orders of magnitude of some invariants of $S$ wit…

math.NT2021

A lower bound for the Wilf density, deduced from a result of Zhai

Michael Hellus, Anton Rechenauer, Rolf Waldi

Let $S \neq = N$ be a numerical semigroup with Frobenius number $f$ , genus $g$ and embedding dimension $e$ . In 1978 Wilf asked the question, whether $\frac{f+1-g}{f+1}\geq\frac…

math.NT2021

Note on a question of Wilf

Michael Hellus, Anton Rechenauer, Rolf Waldi

Let $S$ be a numerical semigroup with Frobenius number $f$ , genus $g$ and embedding dimension $e$ . % In 1978 Wilf asked the question, whether $\frac{f + 1 - g}{f + 1} \geq \frac{1}{e}$ . As is…

math.NT2020★ 1 cited

On the Frobenius number of certain numerical semigroups

Michael Hellus, Anton Rechenauer, Rolf Waldi

Let $0 < λ \leq 1$ , $λ \in / {\frac{2}{4}, \frac{2}{7}, \frac{2}{10}, \frac{2}{13}, \dots}$ , be a real and $p$ a prime number, with $[p, p + λ p]$ containing at least two primes. Denote b…

math.NT2019★ 1 cited

Numerical Semigroups generated by Primes

Michael Hellus, Anton Rechenauer, Rolf Waldi

Let $p_{1} = 2, p_{2} = 3, p_{3} = 5, \dots$ be the consecutive prime numbers, $S_{n}$ the numerical semigroup generated by the primes not less than $p_{n}$ and $u_{n}$ the largest irredundant gene…

math.AC2018

Distributions of weights and a question of Wilf

Michael Hellus, Rolf Waldi

Let $S$ be a numerical semigroup of embedding dimension $e$ and conductor $c$ . The question of Wilf is, if $# (N ∖ S) / c \leq e - 1/ e$ . \noindent In (An asymptotic resul…