Diszkrét matematika = Discrete mathematics

A pályázat résztvevői igen aktívak voltak a 2006-2008 években. Nemcsak sok eredményt értek el, miket több mint 150 cikkben publikáltak, eredményesen népszerűsítették azokat. Több mint 100 konferencián vettek részt és adtak elő, felerészben meghívott, vagy plenáris előadóként. Hagyományos gráfelmélet Több extremális gráfproblémát oldottunk meg. Új eredményeket kaptunk Ramsey számokról, globális és lokális kromatikus számokról, Hamiltonkörök létezéséséről. a crossig numberről, gráf kapacitásokról és kizárt részgráfokról. Véletlen gráfok, nagy gráfok, regularitási lemma Nagy gráfok "hasonlóságait" vizsgáltuk. Különféle metrikák ekvivalensek. Űj eredeményeink: Hereditary Property Testing, Inverse Counting Lemma and the Uniqueness of Hypergraph Limit. Hipergráfok, egyéb kombinatorika Új Sperner tipusú tételekte kaptunk, aszimptotikusan meghatározva a halmazok max számát bizonyos kizárt struktőrák esetén. Több esetre megoldottuk a kizárt hipergráf problémát is. Elméleti számítástudomány Új ujjlenyomat kódokat és bioinformatikai eredményeket kaptunk. | The participants of the project were scientifically very active during the years 2006-2008. They did not only obtain many results, which are contained in their more than 150 papers appeared in strong journals, but effectively disseminated them in the scientific community. They participated and gave lectures in more than 100 conferences (with multiplicity), half of them were plenary or invited talks. Traditional graph theory Several extremal problems for graphs were solved. We obtained new results for certain Ramsey numbers, (local and global) chromatic numbers, existence of Hamiltonian cycles crossing numbers, graph capacities, and excluded subgraphs. Random graphs, large graphs, regularity lemma The "similarities" of large graphs were studied. We show that several different definitions of the metrics (and convergence) are equivalent. Several new results like the Hereditary Property Testing, Inverse Counting Lemma and the Uniqueness of Hypergraph Limit were proved Hypergraphs, other combinatorics New Sperner type theorems were obtained, asymptotically determining the maximum number of sets in a family of subsets with certain excluded configurations. Several cases of the excluded hypergraph problem were solved. Theoretical computer science New fingerprint codes and results in bioinformatics were found

No acute tetrahedron is an 8-reptile

An $r$-gentiling is a dissection of a shape into $r \geq 2$ parts which are all similar to the original shape. An $r$-reptiling is an $r$-gentiling of which all parts are mutually congruent. This article shows that no acute tetrahedron is an $r$-gentile or $r$-reptile for any $r < 9$, by showing that no acute spherical diangle can be dissected into less than nine acute spherical triangles.Comment: updated text, as in press with Discrete Mathematics, Discrete Mathematics Available online 10 November 201

Discrete mathematics

Робоча програма дисципліни “Дискретна математика” для студентів галузі знань 0403 “Системні науки та кібернетика” напряму підготовки 6.040302 “Інформатика”.Рабочая программа дисциплины "Дискретная математика" для студентов области знаний 0403 "Системные науки и кибернетика" направления подготовки 6.040302 "Информатика".Working the course "Discrete mathematics" for students of the field of knowledge 0403 "system sciences and cybernetics" training direction 6.040302 "Information"

Discrete Mathematics

The purpose of the present work is to provide short and supple teaching notes for a $30$ hours introductory course on elementary \textit{Enumerative Algebraic Combinatorics}. We fully adopt the \textit{Rota way} (see, e.g. \cite{KY}). The themes are organized into a suitable sequence that allows us to derive any result from the preceding ones by elementary processes. Definitions of \textit{combinatorial coefficients} are just by their \textit{combinatorial meaning}. The derivation techniques of formulae/results are founded upon constructions and two general and elementary principles/methods: - The \textit{bad element} method (for \textit{recursive} formulae). As the reader should recognize, the bad element method might be regarded as a combinatorial companion of the idea of \textit{conditional probability}. - The \textit{overcounting} principle (for \textit{close form} formulae). Therefore, \textit{no computation} is required in \textit{proofs}: \textit{computation formulae are byproducts of combinatorial constructions}. We tried to provide a self-contained presentation: the only prerequisite is standard high school mathematics. We limited ourselves to the \textit{combinatorial point of view}: we invite the reader to draw the (obvious) \textit{probabilistic interpretations}

Discrete mathematics and its application to ecology

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