By Michael Huber
Due to the type of the finite easy teams, it hasbeen attainable lately to symbolize Steiner t-designs, that's t -(v, ok, 1) designs,mainly for t = 2, admitting teams of automorphisms with sufficiently strongsymmetry houses. although, regardless of the finite basic crew category, forSteiner t-designs with t > 2 every one of these characterizations have remained longstandingchallenging difficulties. specially, 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 guide of IncidenceGeometry, Elsevier technological know-how, Amsterdam, 1995, p. 273), yet possibly datingback to 1965).The current paper maintains the author's paintings (see Huber (J. Comb. conception 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 provide acomplete category of all flag-transitive Steiner 5-designs and end up furthermorethat there are not any non-trivial flag-transitive Steiner 6-designs. either effects depend upon theclassification of the finite 3-homogeneous permutation teams. in addition, we surveysome of the main normal effects on hugely symmetric Steiner t-designs.
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Additional resources for A census of highly symmetric combinatorial designs
Type random segments #Edges Arrangement Size RIG Triang. 8 Table 3: Memory usage (in MBytes) by the point location data structure. 9 Table 4: LM(rand) algorithm performance for a fixed arrangement and a varying number of random landmarks. Figure 5: The average combined (amortized) cost per query in a large arrangement, with 1,366,384 edges. Figure 6: The average breakdown of the time required by the main steps of the Landmarks algorithms in a single point-location query, for arrangements of varying size.
Point is in the current face, also consumes a sigThe main observation of our experiments is nificant part of the query time. This part is the that the Landmarks algorithm is the best stratmajor step of the LM(grid) algorithm. egy considering the cost per query, which takes 23 Arrang. Type random segments #Edges Arrangement Size RIG Triang. 8 Table 3: Memory usage (in MBytes) by the point location data structure. 9 Table 4: LM(rand) algorithm performance for a fixed arrangement and a varying number of random landmarks.
With this motivation, we propose the following measure for representing the shape of a point set under the bounded memory constraint. cluster. Moreover, the locations of these hulls are not determined a priori—rather, as in fc-medians, they are dynamically determined by the algorithm. Unlike kmedians clusters, however, each hull can use a different fraction of the available memory to represent its cluster boundary. One of the key challenges in designing the ClusterHull algorithm is to formulate a good policy for this memory allocation.