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.

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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.