Tag: combinatorics
Alternating and nondeterministic plane-walking automata
summary: Plane-walking automata were introduced by Salo & Törma to recognise languages of two-dimensional infinite words (subshifts), the counterpart of 4-way finite automata for two-dimensional finite words. We extend the model to allow for nondeterminism and alternation of quantifiers. We prove that the recognised subshifts form a strict subclass of sofic ...
À la lumière de quelques propriétés essentielles
Cet exposé consistera en quatre parties, chacune commençant par une introduction à un domaine de recherche et terminant par quelques contributions.
Nous débuterons par expliquer comment la conjecture polynomiale de Hales-Jewett à densité unifie plusieurs des généralisations du théorème de van der Waerden, ainsi que comment cette généralisation commune présente ...
On the intervals of framing lattices
summary: A flow graph \(G\) is an acyclic oriented graph with \(V(G) = [n]\), \(E(G)\) a multi-set of edges where each edge \((i,j)\) satisfies \(i<j\), and such that \(G\) has a unique source \(s=1\) and sink \(t=n\). On such a graph, a route is simply ...
Computability of Compact Spaces
summary: The topological properties of a set have a strong impact on its computability properties. A striking illustration of this idea is given by spheres, closed manifolds and finite graphs without endpoints : if a set X is homeomorphic to a sphere, a closed manifold or such a graph, then any ...
Classes de sous-shifts définis par des formules logiques.
summary: Une configuration est un coloriage du plan Z². Habituellement, les ensembles de configurations étudiés sont ceux définis par un ensemble de motifs "interdits" n'apparaissant dans aucune des configurations de l'ensemble. De tels ensembles sont appelés sous-shifts. Dans ce séminaire, on définit les ensembles de configurations grâce à ...
Manytamaris: on descriptions of the Tamari lattice
summary: Manytamaris is a website about the Tamari lattice. The interest in this particular lattice stems from its many properties, besides being a lattice, and its numerous appearances in different areas of mathematics. As such, the goal for Manytamaris is to be a survey on the descriptions of the Tamari ...
Ranking aggregation: graph-based methods and use in bioinformatics
summary: The problem of ranking aggregation is the following: we have a set of elements and a set of rankings of these elements as input, and we want a single ranking as output, which best reflects the set of rankings taken as input. The applications are manifold, especially in bioinformatics ...
Algèbres tridendriformes, arbres de Schröder et algèbre de Hopf
Les concepts d’algèbres dendriformes, respectivement tridendriformes décrivent l’action de certains éléments du groupe symétrique appelés les battages et respectivement les battages contractants sur l’ensemble des mots dont les lettres sont des éléments d’un alphabet, respectivement d'un monoïde. Un lien entre les algèbres dendriformes et tridendriformes ...
Skipless chain decompositions and improved poset saturation bounds
summary: We show that given m disjoint chains in the Boolean lattice, we can create m disjoint skipless chains that cover the same elements (where we call a chain skipless if any two consecutive elements differ in size by exactly one). By using this result we are able to answer ...
Asymptotic behaviour of cyclic automata
summary: Cyclic dominance describes models where different states (species, strategies...) are in some cyclic prey-predator relationship: for example, rock-paper-scissors. This occurs in many contexts such as ecological systems, evolutionary games on graphs, etc. Many models exhibit heteroclinic cycles where one state dominates almost the whole space before being replaced by ...
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