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We give an alternative proof of W. T. Gowers' theorem on block bases by reducing it to a discrete analogue on specific countable nets. We also give a Ramsey type result on k-tuples of block sequences in a normed linear space with a Schauder basis.

A distance between isomorphism classes of trees

Bohdan Zelinka (1983)

Czechoslovak Mathematical Journal

A divisibility property of binomial coefficients viewed as an elementary sieve.

Hudson, Richard H., Williams, Kenneth S. (1981)

International Journal of Mathematics and Mathematical Sciences

A dual proof of the upper bound conjecture for convex polytopes.

Aage Bondesen, Arne Bronsted (1980)

Mathematica Scandinavica

A duality based proof of the combinatorial nullstellensatz.

Kouba, Omran (2009)

The Electronic Journal of Combinatorics [electronic only]

A factor graph based genetic algorithm

B. Hoda Helmi, Adel T. Rahmani, Martin Pelikan (2014)

International Journal of Applied Mathematics and Computer Science

We propose a new linkage learning genetic algorithm called the Factor Graph based Genetic Algorithm (FGGA). In the FGGA, a factor graph is used to encode the underlying dependencies between variables of the problem. In order to learn the factor graph from a population of potential solutions, a symmetric non-negative matrix factorization is employed to factorize the matrix of pair-wise dependencies. To show the performance of the FGGA, encouraging experimental results on different separable problems...

A family of 4-designs on 26 points

Dragan M. Acketa, Vojislav Mudrinski (1996)

Commentationes Mathematicae Universitatis Carolinae

Using the Kramer-Mesner method, $4$ - $(26, 6, λ)$ designs with $P S L (2, 25)$ as a group of automorphisms and with $λ$ in the set ${30, 51, 60, 81, 90, 111}$ are constructed. The search uses specific partitioning of columns of the orbit incidence matrix, related to so-called “quasi-designs”. Actions of groups $P S L (2, 25)$ , $P G L (2, 25)$ and twisted $P G L (2, 25)$ are being compared. It is shown that there exist $4$ - $(26, 6, λ)$ designs with $P G L (2, 25)$ , respectively twisted $P G L (2, 25)$ as a group of automorphisms and with $λ$ in the set ${51, 60, 81, 90, 111}$ . With $λ$ in the set ${60, 81}$ , there exist designs which possess all three considered groups...

A family of complete arcs in finite projective planes

Barbu C. Kestenband (1989)

Colloquium Mathematicae

A family of nonregular distance monotone graphs

Michel Mollard (1990)

Czechoslovak Mathematical Journal

A Family of Path Properties for Graphs.

E.L. Wilson, R.L. Hemminger, M.D. Plummer (1972)

Mathematische Annalen

A family of tridiagonal pairs related to the quantum affine algebra $U_{q} (\hat{{sl}_{2}})$ .

Alnajjar, Hasan, Curtin, Brian (2005)

ELA. The Electronic Journal of Linear Algebra [electronic only]

A Fan-Type Heavy Pair Of Subgraphs For Pancyclicity Of 2-Connected Graphs

Wojciech Wideł (2016)

Discussiones Mathematicae Graph Theory

Let G be a graph on n vertices and let H be a given graph. We say that G is pancyclic, if it contains cycles of all lengths from 3 up to n, and that it is H-f1-heavy, if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K), dK(u, v) = 2 implies [...] min⁡dG(u),dG(v)≥n+12 $min {d_{G} (u), d_{G} (v)} \geq \frac{n + 1}{2}$ . In this paper we prove that every 2-connected K1,3, P5-f1-heavy graph is pancyclic. This result completes the answer to the problem of finding f1-heavy pairs of subgraphs implying pancyclicity...

A fast algorithm for MacMahon's partition analysis.

Xin, Guoce (2004)

The Electronic Journal of Combinatorics [electronic only]

A fast multi-scale method for drawing large graphs.

Harel, David, Koren, Yehuda (2002)

Journal of Graph Algorithms and Applications

A few more cyclic Steiner 2-designs.

Chen, Kejun, Wei, Ruizhong (2006)

The Electronic Journal of Combinatorics [electronic only]

A few remarks on the history of MST-problem

Jaroslav Nešetřil (1997)

Archivum Mathematicum

On the background of Borůvka’s pioneering work we present a survey of the development related to the Minimum Spanning Tree Problem. We also complement the historical paper Graham-Hell [GH] by a few remarks and provide an update of the extensive literature devoted to this problem.

A Fiedler-like theory for the perturbed Laplacian

Israel Rocha, Vilmar Trevisan (2016)

Czechoslovak Mathematical Journal

The perturbed Laplacian matrix of a graph $G$ is defined as $L^{D} = D - A$ , where $D$ is any diagonal matrix and $A$ is a weighted adjacency matrix of $G$ . We develop a Fiedler-like theory for this matrix, leading to results that are of the same type as those obtained with the algebraic connectivity of a graph. We show a monotonicity theorem for the harmonic eigenfunction corresponding to the second smallest eigenvalue of the perturbed Laplacian matrix over the points of articulation of a graph. Furthermore, we use...

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