Mémoire sur les combinaisons régulières et leurs applications
Après quelques considérations générales sur les relations entre les mathématiques discrètes, l'informatique et l'analyse des données, ce texte présente un ensemble de méthodes utilisant des techniques ordinales ou (et) combinatoires. A une description succinte de chaque méthode sont jointes quelques références relatives à ses aspects théoriques ainsi qu'à ses implémentations accessibles aux utilisateurs. Pour présenter ces méthodes nous les avons classées suivant la nature des tableaux de données...
We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups.We compare characterizations of superrefiexivity in terms of diamond graphs and binary trees.We show that there exist sequences of series-parallel graphs of increasing topological complexitywhich admit uniformly bilipschitz embeddings into a Hilbert space, and thus do not characterize superrefiexivity.
An Abelian scheme corresponds to a special instance of what is usually named a Schur-ring. After the needed results have been quoted on additive codes in Abelian schemes and their duals, coset configurations, coset schemes, metric schemes and distance regular graphs, partition designs and completely regular codes, we give alternative proofs of some of those results. In this way we obtain a construction of metric Abelian schemes and an algorithm to compute their intersection matrices.
Zero forcing number has recently become an interesting graph parameter studied in its own right since its introduction by the “AIM Minimum Rank–Special Graphs Work Group”, whereas metric dimension is a well-known graph parameter. We investigate the metric dimension and the zero forcing number of some line graphs by first determining the metric dimension and the zero forcing number of the line graphs of wheel graphs and the bouquet of circles. We prove that for a simple and connected graph . Further,...
In this paper we consider the point character of metric spaces. This parameter which is a uniform version of dimension, was introduced in the context of uniform spaces in the late seventies by Jan Pelant, Cardinal reflections and point-character of uniformities, Seminar Uniform Spaces (Prague, 1973–1974), Math. Inst. Czech. Acad. Sci., Prague, 1975, pp. 149–158. Here we prove for each cardinal , the existence of a metric space of cardinality and point character . Since the point character can...
Metrically regular bigraphs the square of which are metrically regular graphs are investigated in the case of graphs with 6 distinct eigenvalues (these eigenvalues can have variuos multiplicities).