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Thierry Monteil

Publications and source records attributed to Thierry Monteil.

15 recordsLinked to original sources
arXiv2026

Asymptotic probability of irreducibles III: Anti-SEQ

In this paper, we study the structure of the complete asymptotic expansion of the probability that a large combinatorial object is connected or consists of a given number of connected components. For rapidly growing labeled families of structures, the coefficients involved in these expansions are possibly negative integers. Using species theory, we interpret these coefficients as the difference between the counting sequences of two derivative species of structures. In particular, we show that this difference can be viewed as the counting sequence of the virtual species obtained with the help of an "anti-$\mathrm{SEQ}$" operator applied to the initial family of structures. Applications include $P$-angulated discrete surfaces, quadratic square-tiled surfaces, and non-orientable graph encoded manifolds, which were not reachable with our previous methods. Moving on to the weighted species, we establish the whole structure of the asymptotic expansion of the probability that a graph is connected in the Erd\H{o}s-R\'enyi model $G(n,p)$. Here, the asymptotic coefficients are polynomials in $\frac{p}{1-p}$ and can be described both in terms of simple graphs and irreducible tournaments with ties. We also provide general asymptotic results for sequence and cycle decomposition, as well as the complete asymptotic expansion of the probability that a random labeled tournament with ties is irreducible.

math.CO↗
arXiv2025

Asymptotic probability of irreducibles II: sequence

This paper is devoted to the structure of the complete asymptotic expansion of the probability that a large combinatorial object is irreducible or consists of a given number of irreducible parts, where irreducibility is understood in terms of combinatorial construction SEQ, labeled or unlabeled. We show that for rapidly growing (i.e. gargantuan) combinatorial classes, the coefficients that appear in this expansion are integers and can be interpreted as linear combinations of the counting sequences of three closely related combinatorial classes. We apply this general asymptotic result to labeled and unlabeled (multi-)tournaments, as well as to (multi-)permutations and (multi-)matchings. We also explore the limits of our approach with respect to other combinatorial constructions.

math.CO↗
arXiv2024

Asymptotic probability for connectedness

We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of other derivative combinatorial classes. The general result applies to rapidly growing combinatorial structures, which we call gargantuan, that also admit a sequence decomposition. The result is then applied to several models of graphs, of surfaces (square-tiled surfaces, combinatorial maps), and to geometric models of higher dimension (constellations, graph encoded manifolds). The corresponding derivative combinatorial classes are irreducible (multi)tournaments, indecomposable (multi)permutations and indecomposable perfect (multi)matchings.

math.CO↗
arXiv2022

Asymptotics for connected graphs and irreducible tournaments

We compute the whole asymptotic expansion of the probability that a large uniform labeled graph is connected, and of the probability that a large uniform labeled tournament is irreducible. In both cases, we provide a combinatorial interpretation of the involved coefficients.

math.CO↗
arXiv2017

Capturing the contributions of the semantic web to the IoT: a unifying vision

The Internet of Things (IoT) is a technological topic with a very important societal impact. IoT application domains are various and include: smart cities, precision farming, smart factories, and smart buildings. The diversity of these application domains is the source of the very high technological heterogeneity in the IoT, leading to interoperability issues. The semantic web principles and technologies are more and more adopted as a solution to these interoperability issues, leading to the emergence of a new domain, the Semantic Web Of Things (SWoT). Scientific contributions to the SWoT are many, and the diversity of architectures in which they are expressed complicates comparison. To unify the presented architectures, we propose an architectural pattern, LMU-N. LMU-N provides a reading grid used to classify processes to which the SWoT community contributes, and to describe how the semantic web impacts the IoT. Then, the evolutions of the semantic web to adapt to the IoT constraints are described as well, in order to give a twofold view of the convergence between the IoT and the semantic web toward the SWoT.

cs.CY↗
arXiv2014

Everything is illuminated

We study geometrical properties of translation surfaces: the finite blocking property, bounded blocking property, and illumination properties. These are elementary properties which can be fruitfully studied using the dynamical behavior of the SL(2,R)-action on the moduli space of translation surfaces. We characterize surfaces with the finite blocking property and bounded blocking property, completing work of the second-named author. Concerning the illumination problem, we also extend results of Hubert-Schmoll-Troubetzkoy, removing the hypothesis that the surface in question is a lattice surface, thus settling a conjecture. Our results crucially rely on the recent breakthrough results of Eskin-Mirzakhani and Eskin-Mirzakhani-Mohammadi, and on related results of Wright.

math.DS↗
arXiv2014

Architecting Information Centric ETSI-M2M systems

The European Telecommunications Standards Institute (ETSI) released a set of specifications to define a restful architecture for enabling seamless service provisioning across heterogeneous Machine-to-Machine (M2M) systems. The current version of this architecture is strongly centralized, thus requiring new enhancements to its scalability, fault tolerance, and flexibility. To bridge this gap, herein it is presented an Overlay Service Capability Layer, based on Information Centric Networking design. Key features, example use cases and preliminary performance assessments are also discussed to highlight the potential of our approach.

cs.NI↗
arXiv2013

Symmetric Determinantal Representations in Characteristic 2

This paper studies Symmetric Determinantal Representations (SDR) in characteristic 2, that is the representation of a multivariate polynomial P by a symmetric matrix M such that P=det(M), and where each entry of M is either a constant or a variable. We first give some sufficient conditions for a polynomial to have an SDR. We then give a non-trivial necessary condition, which implies that some polynomials have no SDR, answering a question of Grenet et al. A large part of the paper is then devoted to the case of multilinear polynomials. We prove that the existence of an SDR for a multilinear polynomial is equivalent to the existence of a factorization of the polynomial in certain quotient rings. We develop some algorithms to test the factorizability in these rings and use them to find SDRs when they exist. Altogether, this gives us polynomial-time algorithms to factorize the polynomials in the quotient rings and to build SDRs. We conclude by describing the case of Alternating Determinantal Representations in any characteristic.

cs.CC↗
arXiv2011

The complexity of tangent words

In a previous paper, we described the set of words that appear in the coding of smooth (resp. analytic) curves at arbitrary small scale. The aim of this paper is to compute the complexity of those languages.

cs.DM↗
arXiv2008

Finite blocking property versus pure periodicity

A translation surface S is said to have the finite blocking property if for every pair (O,A) of points in S there exists a finite number of "blocking" points B_1,...,B_n such that every geodesic from O to A meets one of the B_i's. S is said to be purely periodic if the directional flow is periodic in each direction whose directional flow contains a periodic trajectory (this implies that S admits a cylinder decomposition in such directions). We will prove that finite blocking property implies pure periodicity. We will also classify the surfaces that have the finite blocking property in genus 2: such surfaces are exactly the torus branched coverings. Moreover, we prove that in every stratum, such surfaces form a set of null measure. In the Appendix, we prove that completely periodic translation surfaces form a set of null measure in every stratum.

math.DS↗
arXiv2006

Quasiperiodic infinite words : multi-scale case and dynamical properties

An infinite word x is said to be quasiperiodic if there exists a finite word q such that x is covered by occurrences of q (such a q is called a quasiperiod of x). Using the notion of derivation, we show that this definition is not sufficient to imply any symmetry in an infinite word. Therefore we introduce multi-scale quasiperiodic words, i.e. quasiperiodic words that admit an infinite number of quasiperiods. Such words are uniformly recurrent, this allows us to study the subshift they generate. We prove that multi-scale quasiperiodic subshifts are uniquely ergodic and have zero topological entropy as well as zero Kolmogorov complexity. Sturmian subshifts are shown to be multi-scale quasiperiodic.

math.DS↗
arXiv2004

A counter-example to the theorem of Hiemer and Snurnikov

A planar polygonal billiard $¶$ is said to have the finite blocking property if for every pair $(O,A)$ of points in $¶$ there exists a finite number of ``blocking'' points $B_1, ..., B_n$ such that every billiard trajectory from $O$ to $A$ meets one of the $B_i$'s. As a counter-example to a theorem of Hiemer and Snurnikov, we construct a family of rational billiards that lack the finite blocking property.

math.DS↗
arXiv2004

On the finite blocking property

A planar polygonal billiard $¶$ is said to have the finite blocking property if for every pair $(O,A)$ of points in $¶$ there exists a finite number of ``blocking'' points $B_1, ..., B_n$ such that every billiard trajectory from $O$ to $A$ meets one of the $B_i$'s. Generalizing our construction of a counter-example to a theorem of Hiemer and Snurnikov (see \cite{Mo}), we show that the only regular polygons that have the finite blocking property are the square, the equilateral triangle and the hexagon. Then we extend this result to translation surfaces. We prove that the only Veech surfaces with the finite blocking property are the torus branched coverings. We also provide a local sufficient condition for a translation surface to fail the finite blocking property. This enables us to give a complete classification for the L-shaped surfaces as well as to obtain a density result in the space of translation surfaces in every genus $g\geq 2$.

math.DS↗