A census of highly symmetric combinatorial designs by Michael Huber

By Michael Huber

Due to the class of the finite basic teams, it hasbeen attainable in recent times to signify Steiner t-designs, that's t -(v, okay, 1) designs,mainly for t = 2, admitting teams of automorphisms with sufficiently strongsymmetry houses. notwithstanding, regardless of the finite uncomplicated team type, forSteiner t-designs with t > 2 almost all these characterizations have remained longstandingchallenging difficulties. in particular, the decision of all flag-transitiveSteiner t-designs with three ≤ t ≤ 6 is of specific curiosity and has been open for about40 years (cf. Delandtsheer (Geom. Dedicata forty-one, p. 147, 1992 and instruction manual of IncidenceGeometry, Elsevier technology, Amsterdam, 1995, p. 273), yet possibly datingback to 1965).The current paper maintains the author's paintings (see Huber (J. Comb. concept Ser.A ninety four, 180-190, 2001; Adv. Geom. five, 195-221, 2005; J. Algebr. Comb., 2007, toappear)) of classifying all flag-transitive Steiner 3-designs and 4-designs. We supply acomplete category of all flag-transitive Steiner 5-designs and turn out furthermorethat there are not any non-trivial flag-transitive Steiner 6-designs. either effects depend on theclassification of the finite 3-homogeneous permutation teams. in addition, we surveysome of the main basic effects on hugely symmetric Steiner t-designs.

Show description

Read or Download A census of highly symmetric combinatorial designs PDF

Similar combinatorics books

Applications of Unitary Symmetry And Combinatorics

A concise description of the prestige of a desirable medical challenge - the inverse variational challenge in classical mechanics. The essence of this challenge is as follows: one is given a collection of equations of movement describing a undeniable classical mechanical procedure, and the query to be replied is: do those equations of movement correspond to a few Lagrange functionality as its Euler-Lagrange equations?

Analysis and Logic

This quantity provides articles from 4 awesome researchers who paintings on the cusp of research and good judgment. The emphasis is on lively study themes; many effects are offered that experience now not been released earlier than and open difficulties are formulated. significant attempt has been made by means of the authors to make their articles obtainable to mathematicians new to the realm

Notes on Combinatorics

Méthodes mathématiques de l’informatique II, college of Fribourg, Spring 2007, model 24 Apr 2007

Optimal interconnection trees in the plane : theory, algorithms and applications

This e-book explores basic points of geometric community optimisation with purposes to numerous actual global difficulties. It provides, for the 1st time within the literature, a cohesive mathematical framework in which the homes of such optimum interconnection networks may be understood throughout quite a lot of metrics and value capabilities.

Additional info for A census of highly symmetric combinatorial designs

Sample text

Ukkonen. On-line construction of suffix trees. Algorithmica, 14:249–260, 1995. 32. P. Weiner. Linear pattern matching. In Proc. 14th IEEE Symp. on Switching and Automata Theory, pages 1–11. IEEE, 1973. kr Abstract. The compressed suffix array and the compressed suffix tree for a given string S are full-text index data structures occupying O(n log |Σ|) bits where n is the length of S and Σ is the alphabet from which symbols of S are drawn. When they were first introduced, they were constructed from suffix arrays and suffix trees, which implies they were not constructed in optimal O(n log |Σ|)-bit working space.

Let x be a leaf in eti (S)P with label (id s , l) corresponding to a string s ∈ S. There exists t pref s with d(t, P ) = i if and only if l ≤ |P |. Thus, not all leaves found in eti (S)P correspond to i-error occurrences of P . To locate the correct leaves, we use range queries, see Section 6. 3. Finally, if P matches a prefix t of some string s ∈ S with exactly i errors, then there is a dichotomy. Let ρ(P, t) = (op 1 , op 2 , . . , op i ) be an ordered edit sequence. , a prefix p pref P of length |p| > hj is found in etj (S) and etj (S)p contains a leaf x with label (id s , l).

ACM Press, 2000. 4. A. Borodin, R. Ostrovsky, and Y. Rabani. Lower bounds for high dimensional nearest neighbor search and related problems. In Proc. 31st ACM Symp. on Theory of Computing (STOC), pages 312–321. ACM Press, 1999. 5. G. S. Brodal and L. G¸asieniec. Approximate dictionary queries. In Proc. 7th Symp. on Combinatorial Pattern Matching (CPM), volume 1075 of LNCS, pages 65–74, 1996. 6. A. L. Buchsbaum, M. T. Goodrich, and J. Westbrook. Range searching over tree cross products. In Proc.

Download PDF sample

Rated 4.00 of 5 – based on 15 votes