Estimating the sequence of real binomial coefficients.
Estimation of cut-vertices in edge-coloured complete graphs
Estimation of the index of
Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix.
Estrada index of iterated line graphs
Eternal Domination: Criticality and Reachability
We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached. The study of the stronger assertion that such a set can be reached after a single attack is defended leads to the study of graphs which are critical in the sense that deleting any vertex reduces the eternal domination number. Examples of these graphs and tight...
Étude des tresses de Gutmann en algèbre à valeurs
La notion de tresse de Gutmann a été introduite ([4]) pour généraliser la notion de chaîne de Gutmann qui restait souvent assez loin du protocole observé. Les tresses de Gutmann ont été étudiées ([3], [4], [6]) en considérant que les réponses au questionnaire étaient dichotomiques. Nous supposons ici que les réponses aux questions appartiennent à un ensemble fini totalement ordonné quelconque.
Etude du spectre pour certains noyaux sur un arbre
Etude sur les plans en blocs incomplets equilibres
Eulerian calculus. IV: Specializations.
Eulerian numbers and operators.
Eulerian numbers, Foulkes characters and Lefschetz characters of the symmetric group.
Eulerian numbers with fractional order parameters.
Eulerian polar graphs
Euler-Mahonian parameters on colored permutation groups.
Eulerovy čtverce
Euler's idoneal numbers and an inequality concerning minimal graphs with a prescribed number of spanning trees
Let be the least number for which there exists a simple graph with vertices having precisely spanning trees. Similarly, define as the least number for which there exists a simple graph with edges having precisely spanning trees. As an -cycle has exactly spanning trees, it follows that . In this paper, we show that and if and only if , which is a subset of Euler’s idoneal numbers. Moreover, if and we show that and This improves some previously estabilished bounds.
Euler’s Partition Theorem
In this article we prove the Euler’s Partition Theorem which states that the number of integer partitions with odd parts equals the number of partitions with distinct parts. The formalization follows H.S. Wilf’s lecture notes [28] (see also [1]). Euler’s Partition Theorem is listed as item #45 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/ [27].
Euler-Seidel matrices. (Matrices d'Euler-Seidel.)
Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence
In this paper we use the Euler-Seidel method for deriving new identities for hyperharmonic and r-Stirling numbers. The exponential generating function is determined for hyperharmonic numbers, which result is a generalization of Gosper’s identity. A classification of second order recurrence sequences is also given with the help of this method.