23 citations · 45 across the 17 of their papers we have counts for
21 papers
Does the problem of the Nile have a solution?
Guillaume Chèze, François Ollivier
The problem of the Nile has been stated by R. Fisher in 1936. This problem concerns the fair division of an agricultural land and is the eponymous problem of a general class of pro…
Between proportionnality and envy-freeness: k-proportionality
Guillaume Chèze
This article deals with the cake cutting problem. In this setting, there exists two notions of fair division: proportional division (when there are n players, each player thinks to…
The Inversion Paradox and Ranking Methods in Tournaments
Guillaume Chéze, Etienne Fieux
This article deals with ranking methods. We study the situation where a tournament between players , , \ldots gives the ranking $P_1 \succ P_2 \succ \cdots \suc…
Envy-free cake cutting: A polynomial number of queries with high probability
Guillaume Chèze
In this article we propose a probabilistic framework in order to study the fair division of a divisible good, e.g., a cake, between n players. Our framework follows the same idea t…
Cake cutting: Explicit examples for impossibility results
Guillaume Chèze
In this article we suggest a model of computation for the cake cutting problem. In this model the mediator can ask the same queries as in the Robertson-Webb model but he or she can…
How to share a cake with a secret agent
Guillaume Chèze
In this note we study a problem of fair division in the absence of full information. We give an algorithm which solves the following problem: n 2 persons want to cut a cake i…
Don't cry to be the first!Symmetric fair division exist
Guillaume Chèze
In this article we study a cake cutting problem. More precisely, we study symmetric fair division algorithms, that is to say we study algorithms where the order of the players do n…
Symbolic Computations of First Integrals for Polynomial Vector Fields
Guillaume Chèze, Thierry Combot
In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for…
How to cut a cake with a gram matrix
Guillaume Chèze, Luca Amodei
In this article we study the problem of fair division. In particular we study a notion introduced by J. Barbanel that generalizes super envy-free fair division. We give a new proof…
Existence of a simple and equitable fair division: a short proof
Guillaume Chèze
In this note we study how to share a good between n players in a simple and equitable way. We give a short proof for the existence of such fair divisions.
Topological aggregation, the twin paradox and the no show paradox
Guillaume Chèze
Consider the framework of topological aggregation introduced by Chichilnisky (1980). We prove that in this framework the Twin Paradox and the No Show Paradox cannot be avoided. Ano…
Efficient Algorithms for Computing Rational First Integrals and Darboux Polynomials of Planar Polynomial Vector Fields
Alin Bostan, Guillaume Chèze, Thomas Cluzeau +1
We present fast algorithms for computing rational first integrals with bounded degree of a planar polynomial vector field. Our approach is inspired by an idea of Ferragut and Giaco…
Bounding the number of remarkable values via Jouanolou's theorem
Guillaume Chèze
In this article we bound the number of remarkable values of a polynomial vector field. The proof is short and based on Jouanolou's theorem about rational first integrals of planar…
Darboux theory of integrability in the sparse case
Guillaume Chèze
Darboux's theorem and Jouanolou's theorem deal with the existence of first integrals and rational first integrals of a polynomial vector field. These results are given in terms of…
Specializations of indecomposable polynomials
Arnaud Bodin, Guillaume Chéze, Pierre Débes
We address some questions concerning indecomposable polynomials and their behaviour under specialization. For instance we give a bound on a prime for the reduction modulo o…
A recombination algorithm for the decomposition of multivariate rational functions
Guillaume Chèze
In this paper we show how we can compute in a deterministic way the decomposition of a multivariate rational function with a recombination strategy. The key point of our recombinat…
Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time
Guillaume Chèze
In this paper we study planar polynomial differential systems of this form: dX/dt=A(X, Y), dY/dt= B(X, Y), where A,B belongs to Z[X, Y], degA \leq d, degB \leq d, and the height of…
Nearly Optimal Algorithms for the Decomposition of Multivariate Rational Functions and the Extended Lüroth's Theorem
Guillaume Chèze
The extended Lüroth's Theorem says that if the transcendence degree of $\KK(\mathsf{f}_1,\dots,\mathsf{f}_m)/\KK$ is 1 then there exists $f \in \KK(\underline{X})$ such that $\KK(\…
Modular Las Vegas Algorithms for Polynomial Absolute Factorization
Cristina Bertone, Guillaume Chèze, André Galligo
Let $f(X,Y) \in \ZZ[X,Y]$ be an irreducible polynomial over $\QQ$. We give a Las Vegas absolute irreducibility test based on a property of the Newton polytope of , or more preci…
Noether's forms for the study of non-composite rational functions and their spectrum
Laurent Busé, Guillaume Chèze, Salah Najib
In this paper, the spectrum and the decomposability of a multivariate rational function are studied by means of the effective Noether's irreducibility theorem given by Ruppert. Wit…
On the total order of reducibility of a pencil of algebraic plane curves
Laurent Busé, Guillaume Chèze
In this paper, the problem of bounding the number of reducible curves in a pencil of algebraic plane curves is addressed. Unlike most of the previous related works, each reducible…