Mathematical Methods in Computer Science: Essays in Memory by Giovanni Di Crescenzo (auth.), Jacques Calmet, Willi

By Giovanni Di Crescenzo (auth.), Jacques Calmet, Willi Geiselmann, Jörn Müller-Quade (eds.)

This Festschrift quantity includes the complaints of the convention Mathematical equipment in machine technological know-how, MMICS 2008, which was once held in the course of December 17-19, 2008, in Karlsruhe, Germany, in reminiscence of Thomas Beth.

The topics of the convention mirrored the various pursuits of Thomas Beth. even though, those pursuits might sound varied, mathematical equipment and particularly algebra as a language constituted the typical denominator of all of his medical achievements.

The 12 contributed talks offered have been rigorously chosen from 30 submissions and canopy the subjects cryptography, designs, quantum computing, algorithms, and coding conception. moreover, this quantity comprises invited talks held on the convention. One specializes in the world of coding idea and symbolic computation, a space specially preferred by means of Thomas Beth, since it combines algebra and algorithmics. the opposite one discusses quantum details, which back used to be a spotlight of Thomas Beth’s examine.

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Springer, Heidelberg (1996) 18. : An examination of the different possible solutions of a problem in incomplete blocks. Ann. Eugenics 10, 52–75 (1940) 19. : Finite Simple Groups. An Introduction to Their Classification. , New York (1982) 20. : Combinatorial Theory, 2nd edn. J. Wiley, New York (1986) 21. : Geometric ABA-groups. Illinois J. Math. 5, 382– 397 (1961) 22. : Classification of flag-transitive Steiner quadruple systems. J. Combin. Theory, Series A 94, 180–190 (2001) 23. : The classification of flag-transitive Steiner 3-designs.

Now an optimal solution for each row Mi,· of the binary linear program corresponds to a maximum weight clique in G. Again there exist heuristics and exact algorithms to determine maximum weight cliques in graphs. g. CLIQUER [16]. This approach allows to use clique bounds from algebraic graph theory to obtain upper bounds on the target function f (x). In the case where we are able to locate large independent sets in G which are not subsets of the Ci we can use them to add further inequalities to (7).

4]). ” We first state (cf. [49]): 22 M. Huber Proposition 2. Let t be a positive integer, and G a finite (abstract) group. Then there is a t-design such that the full group Aut(D) of automorphisms has a subgroup isomorphic to G. One of the early important results regarding highly symmetric designs is due to R. Block [3, Thm. 2]: Proposition 3. (Block 1965). Let D = (X, B, I) be a non-trivial t-(v, k, λ) design with t ≥ 2. If G ≤ Aut(D) acts block-transitively on D, then G acts pointtransitively on D.

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