Jonathan Chappelon

activity

20082026

most citedMöbius function of semigroup posets through Hilbert series

5 citations · 27 across the 19 of their papers we have counts for

collaborators

21 papers

cs.DM2026

A new proof of Delahan's induced-universality result

Jonathan Chappelon

We give a short and self-contained proof of Delahan's theorem stating that every simple graph on $n$ vertices occurs as an induced subgraph of a Steinhaus graph on $\frac{n(n-1)}{2…

math.CO2025

Balanced Steinhaus triangles

Jonathan Chappelon

A Steinhaus triangle modulo $m$ is a finite down-pointing triangle of elements in the finite cyclic group $Z / m Z$ satisfying the same local rule as the standard Pa…

math.AC2025

Numerical semigroup tree: type-representation

Jonathan Chappelon, Jorge L. Ramírez Alfonsín, Dumitru I. Stamate

In this paper, we introduce a new depicting of the so-called numerical semigroup tree $T$ . By exploring computationally this improved picture, relying on the type notion o…

math.NT2020

The Square Frobenius Number

Jonathan Chappelon, Jorge Luis Ramírez Alfonsín

Let $S = ⟨ s_{1}, \dots, s_{n} ⟩$ be a numerical semigroup generated by the relatively prime positive integers $s_{1}, \dots, s_{n}$ . Let $k ⩾ 2$ be an integer. In…

cs.DM2019

Symmetric binary Steinhaus triangles and parity-regular Steinhaus graphs

Jonathan Chappelon

A binary Steinhaus triangle is a triangle of zeroes and ones that points down and with the same local rule as the Pascal triangle modulo 2. A binary Steinhaus triangle is said to b…

math.CO2017

Periodic balanced binary triangles

Jonathan Chappelon

A binary triangle of size $n$ is a triangle of zeroes and ones, with $n$ rows, built with the same local rule as the standard Pascal triangle modulo $2$ . A binary triangle is said…

math.CO2016

Codimension two and three Kneser Transversals

Jonathan Chappelon, Leonardo Martínez-Sandoval, Luis Montejano +2

Let $k, d, λ ⩾ 1$ be integers with $d ⩾ λ$ and let $X$ be a finite set of points in $R^{d}$ . A $(d - λ)$ -plane $L$ transversal to the convex hulls of all $k$ -set…

cs.GT2015

Two-Player Tower of Hanoi

Jonathan Chappelon, Urban Larsson, Akihiro Matsuura

The Tower of Hanoi game is a classical puzzle in recreational mathematics (Lucas 1883) which also has a strong record in pure mathematics. In a borderland between these two areas w…

math.GR2014★ 5 cited

Möbius function of semigroup posets through Hilbert series

Jonathan Chappelon, Ignacio García-Marco, Luis Pedro Montejano +1

In this paper, we investigate the M{ö}bius function $μ_S$ associated to a (locally finite) poset arising from a semigroup $S$ of $Z^{m}$ . We introduce…

math.CO2014★ 2 cited

Balanced simplices

Jonathan Chappelon

An additive cellular automaton is a linear map on the set of infinite multidimensional arrays of elements in a finite cyclic group $Z / m Z$ . In this paper, we consi…

math.CO2013★ 1 cited

On Ramsey numbers of complete graphs with dropped stars

Jonathan Chappelon, Luis Pedro Montejano, Jorge Ramírez Alfonsín

Let $r (G, H)$ be the smallest integer $N$ such that for any $2$ -coloring (say, red and blue) of the edges of $K_n$ , $n ⩾ N$ , there is either a red copy of $G$ or a blue copy…

math.CO2013

Ramsey for complete graphs with dropped cliques

Jonathan Chappelon, Luis Pedro Montejano, Jorge Luis Ramírez Alfonsín

Let $K_[k, t]$ be the complete graph on $k$ vertices from which a set of edges, induced by a clique of order $t$ , has been dropped. In this note we give two explicit upper bounds…

math.CO2013

Modular Schur numbers

Jonathan Chappelon, María Pastora Revuelta Marchena, María Isabel Sanz Domínguez

For any positive integers l and m, a set of integers is said to be (weakly) l-sum-free modulo m if it contains no (pairwise distinct) elements $x_{1}, x_{2}, ..., x_{l}, y$ satisfying the co…

math.CO2013

Connected covering numbers

Jonathan Chappelon, Kolja Knauer, Luis Pedro Montejano +1

A connected covering is a design system in which the corresponding {\em block graph} is connected. The minimum size of such coverings are called {\em connected coverings numbers}.…

math.CO2012★ 4 cited

On the Möbius function of the locally finite poset associated with a numerical semigroup

Jonathan Chappelon, Jorge Ramírez Alfonsín

Let $S$ be a numerical semigroup and let $(Z, ⩽_S)$ be the (locally finite) poset induced by $S$ on the set of integers $Z$ defined by $x \leqs…

math.CO2011★ 3 cited

On the problem of Molluzzo for the modulus 4

Jonathan Chappelon, Shalom Eliahou

We solve the currently smallest open case in the 1976 problem of Molluzzo on $Z / m Z$ , namely the case $m = 4$ . This amounts to constructing, for all positive integer…

math.NT2010★ 3 cited

On generalized Frame-Stewart numbers

Jonathan Chappelon, Akihiro Matsuura

For the multi-peg Tower of Hanoi problem with $k ⩾ 4$ pegs, so far the best solution is obtained by the Stewart's algorithm based on the the following recurrence relation:…

math.CO2009★ 5 cited

A universal sequence of integers generating balanced Steinhaus figures modulo an odd number

Jonathan Chappelon

In this paper, we partially solve an open problem, due to J.C. Molluzzo in 1976, on the existence of balanced Steinhaus triangles modulo a positive integer $n$ , that are Steinhaus…

math.NT2009

On the multiplicative order of $a^{n}$ modulo $n$

Jonathan Chappelon

Let $n$ be a positive integer and $α_{n}$ be the arithmetic function which assigns the multiplicative order of $a^{n}$ modulo $n$ to every integer $a$ coprime to $n$ and vanishes elsew…

math.CO2008★ 3 cited

Regular Steinhaus graphs of odd degree

Jonathan Chappelon

A Steinhaus matrix is a binary square matrix of size $n$ which is symmetric, with diagonal of zeros, and whose upper-triangular coefficients satisfy $a_{i, j} = a_{i - 1, j - 1} + a_{i - 1, j}$ …

math.CO2008★ 1 cited

On a problem of Molluzzo concerning Steinhaus triangles in finite cyclic groups

Jonathan Chappelon

Let $X$ be a finite sequence of length $m \geq 1$ in $Z / n Z$ . The \textit{derived sequence} $\partial X$ of $X$ is the sequence of length $m - 1$ obtained by pairwise…

A new proof of Delahan's induced-universality result

Balanced Steinhaus triangles

Numerical semigroup tree: type-representation

The Square Frobenius Number

Symmetric binary Steinhaus triangles and parity-regular Steinhaus graphs

Periodic balanced binary triangles

Codimension two and three Kneser Transversals

Two-Player Tower of Hanoi

Möbius function of semigroup posets through Hilbert series

Balanced simplices

On Ramsey numbers of complete graphs with dropped stars

Ramsey for complete graphs with dropped cliques

Modular Schur numbers

Connected covering numbers

On the Möbius function of the locally finite poset associated with a numerical semigroup

On the problem of Molluzzo for the modulus 4

On generalized Frame-Stewart numbers

A universal sequence of integers generating balanced Steinhaus figures modulo an odd number

On the multiplicative order of an modulo n

Regular Steinhaus graphs of odd degree

On a problem of Molluzzo concerning Steinhaus triangles in finite cyclic groups

On the multiplicative order of $a^{n}$ modulo $n$