29 citations · 43 across the 8 of their papers we have counts for
8 papers
Criteria for a split real polynomial
Jean-Michel Billiot, Eric Fontenas
In this article, we establish necessary and sufficient conditions for a polynomial of degree to have exactly real roots. A complete study of polynomials of degree five is c…
An iterative approach for real roots of polynomials
J. -M Billiot, E Fontenas
In the present study, we propose necessary and sufficient assumptions on the coefficients in order to only get distinct real roots of polynomials.
Continuum Percolation in the Relative Neighborhood Graph
Jean-Michel Billiot, Franck Corset, Eric Fontenas
In the present study, we establish the existence of nontrivial site percolation threshold in the Relative Neighborhood Graph (RNG) for Poisson stationary point process with unit in…
On uniqueness of the q-state Potts model on a self-dual family of graphs
Jean-Michel Billiot, Franck Corset, Eric Fontenas
This paper deals with the location of the complex zeros of the Tutte polynomial for a class of self-dual graphs. For this class of graphs, as the form of the eigenvalues is known,…
Maximum pseudolikelihood estimator for exponential family models of marked Gibbs point processes
Jean-Michel Billiot, Jean-François Coeurjolly, Rémy Drouilhet
This paper is devoted to the estimation of a vector parametrizing an energy function of a Gibbs point process, via the maximum pseudolikelihood method. Strong consistency a…
On the number of clusters for planar graphs
Jean-Michel Billiot, Franck Corset, Eric Fontenas
The Tutte polynomial is a powerfull analytic tool to study the structure of planar graphs. In this paper, we establish some relations between the number of clusters per bond for pl…