A finite embedding theorem for partial Steiner 3-designs
نویسندگان
چکیده
منابع مشابه
Embedding Partial Steiner Triple Systems
We prove that a partial Steiner triple system 8 of order n can be embedded in a Steiner triple system T of any given admissible order greater than 4w. Furthermore, if G(S), the missing-edge graph of S, has the property that A(G)<ri(n + l)l and \E(G)\ then # can be embedded in a Steiner triple system of order 2n +1, provided that 2w +1 is admissible. We also prove that if there is a partial Stei...
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The system has the nice property that any pair of distinct elements of V occurs in exactly one of the subsets. This makes it an example of a Steiner triple system. Steiner triple systems first appeared in the mathematical literature in the mid-nineteenth century but the concept must surely have been thought of long before then. An excellent historical introduction appears in [7]. As pointed out...
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Let q be a prime power and a be a positive integer such that a 2. Assume that there is a Steiner 3-(a+1, q+1, 1) design. For every v satisfying certain arithmetic conditions we can construct a Steiner 3-(va+1, q+1, 1) design for every d sufficiently large. In the case of block size 6, when q=5, this theorem yields new infinite families of Steiner 3-designs: if v is a given positive integer sati...
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It is shown that there is a function g on the natural numbers such that a partial Steiner triple system U on u points can be embedded in a Steiner triple system V on v points, in such a way that all automorphisms of U can be extended to V , for every admissible v satisfying v > g(u). We find exponential upper and lower bounds for g.
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In the 1970’s Paul Erdős and Dominic Welsh independently posed the problem of whether all finite partial linear spaces L are embeddable in finite projective planes. Except for the case when L has a unique embedding in a projective plane with few additional points, very little has been done which is directly applicable to this problem. In this paper it is proved that every finite partial linear ...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2015
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2014.09.011