Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 10 of 10 for “"combinatorial designs"”.
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Combinatorial designs and their automorphism groups
This thesis concerns the automorphism groups of Steiner triple systems and of cycle systems. Although most Steiner triple systems have trivial automorphism groups [2], it is widely known that for every abstract group, there exists a Steiner triple system whose automorphism is isomorphic to that …
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Coloring Problems on Graphs and Hypergraphs
… r-edge-coloring of K n is not (r, m)-splittable. Combinatorial designs yield fr(m) ≤ O(r2m2). Extending ideas of Erdo&huml;s and Gyarfas yields f r(m) ≥ min{O(rm 2), O(r2m)}. Similar bounds hold for a generalization to hypergraphs.
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An Introduction to S(5,8,24)
… the largest known Steiner systems and connects combinatorial designs, error-correcting codes, finite simple groups, and sphere packings in a truly remarkable way. This thesis discusses the underlying structure of S(5,8,24), its construction via the (24,12) Golay code, as well its automorphism …
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Random and exact structures in combinatorics
… such notions come into play in the study of combinatorial probability and the use of random processes in extremal combinatorics. In a broader view, randomness (and the pseudorandomness notions which resemble it along various axes) can be viewed as a type of structure in and of itself which …
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Combinatorial Methods in the Representation Theory of the Symmetric Group
… of the symmetric group can be carried out from a combinatorial point of view, avoiding the machinery of the representation theory of algebraic groups. This approach has the benefit of providing more insight into the subject as the study remains in the setting of the symmetric group. A number of …
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A characterization of the circularity of certain balanced incomplete block designs.
… We devote a chapter to the use of circular designs in coding theory. It is proven that these structures are not useful in the theory of error-correcting codes, since more efficient codes are known, for example the Reed-Muller codes. However, the theory developed in the earlier chapters does …
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Reducibility and Statistical-Computational Gaps from Secret Leakage
… techniques that also reveal novel connections to combinatorial designs based on the incidence geometry of Fᵗᵣ and to random matrix theory. In particular, we show a convergence result between Wishart and inverse Wishart matrices that may be of independent interest. The specific hardness conjectures …
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Double-Change Covering Designs with Block Size k = 4
… is to minimize b for a fixed v and k. Tight designs are those in which each pair is covered exactly once. We present constructions of tight dccd’s for arbitrary v when k = 2 and minimal constructions for v <= 20 when k = 4. A general, but not minimal, method is presented to construct circular …