364,200 research outputs found
On the existence of block-transitive combinatorial designs
Block-transitive Steiner -designs form a central part of the study of
highly symmetric combinatorial configurations at the interface of several
disciplines, including group theory, geometry, combinatorics, coding and
information theory, and cryptography. The main result of the paper settles an
important open question: There exist no non-trivial examples with (or
larger). The proof is based on the classification of the finite 3-homogeneous
permutation groups, itself relying on the finite simple group classification.Comment: 9 pages; to appear in "Discrete Mathematics and Theoretical Computer
Science (DMTCS)
Steiner t-designs for large t
One of the most central and long-standing open questions in combinatorial
design theory concerns the existence of Steiner t-designs for large values of
t. Although in his classical 1987 paper, L. Teirlinck has shown that
non-trivial t-designs exist for all values of t, no non-trivial Steiner
t-design with t > 5 has been constructed until now. Understandingly, the case t
= 6 has received considerable attention. There has been recent progress
concerning the existence of highly symmetric Steiner 6-designs: It is shown in
[M. Huber, J. Algebr. Comb. 26 (2007), pp. 453-476] that no non-trivial
flag-transitive Steiner 6-design can exist. In this paper, we announce that
essentially also no block-transitive Steiner 6-design can exist.Comment: 9 pages; to appear in: Mathematical Methods in Computer Science 2008,
ed. by J.Calmet, W.Geiselmann, J.Mueller-Quade, Springer Lecture Notes in
Computer Scienc
Resolvable designs with large blocks
Resolvable designs with two blocks per replicate are studied from an
optimality perspective. Because in practice the number of replicates is
typically less than the number of treatments, arguments can be based on the
dual of the information matrix and consequently given in terms of block
concurrences. Equalizing block concurrences for given block sizes is often, but
not always, the best strategy. Sufficient conditions are established for
various strong optimalities and a detailed study of E-optimality is offered,
including a characterization of the E-optimal class. Optimal designs are found
to correspond to balanced arrays and an affine-like generalization.Comment: Published at http://dx.doi.org/10.1214/009053606000001253 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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