Matthieu Dufour

activity

20122026

collaborators

8 papers

math.CO2026

Necklace Games

Balaji R. Kadam, Silvia Heubach, Matthieu Dufour

We define and give results on the game NecklaceNim NN( $n$ , $k$ ) which is PathNim PN( $n$ , $k$ ) with an additional move allowed on the end vertices. This game arises as a sub-game in t…

math.CO2026

The Invariance Reduction Process -- a New Tool to Solve Circular Nim and Related Games

Balaji R. Kadam, Matthieu Dufour, Silvia Heubach

We introduce the notion of invariant vectors of a game and develop the Invariance Reduction Process, which first uses reduction of positions via invariance and then zero and merge…

math.CO2024

On the $P$ -positions of some infinite families of Slow $A$ -Nim

Silvia Heubach, Matthieu Dufour

We introduce the game Slow $A$ -Nim which generalizes a number of recently studied games. Slow $A$ -Nim is played on $n$ stacks of tokens, and the set $A$ indicates the number of sta…

math.CO2021

Circular Nim CN(7,4)

Matthieu Dufour, Silvia Heubach

Circular Nim is a two-player impartial combinatorial game consisting of $n$ stacks of tokens placed in a circle. A move consists of choosing $k$ consecutive stacks and taking at le…

math.ST2020

A class of copulae associated with Brownian motion processes and their maxima

Michel Adès, Matthieu Dufour, Serge B. Provost +1

The main objective of this paper consists in creating a new class of copulae from various joint distributions occurring in connection with certain Brownian motion processes. We foc…

math.CO2016

A misère play $⋆$ -operator

Matthieu Dufour, Silvia Heubach, Urban Larsson

We study the $⋆$ -operator (Larsson et al. 2011) of impartial vector subtraction games (Golomb 1965). Here we extend the notion to the misère-play convention, and prove converge…

cs.DM2015

Building Nim

Eric Duchêne, Matthieu Dufour, Silvia Heubach +1

The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizatio…

math.CO2012

Circular Nim Games