منابع مشابه
An Enumeration of Graphical Designs
Let Ψ(t, k) denote the set of pairs (v, λ) for which there exists a graphical t-(v, k, λ) design. Most results on graphical designs have gone to show the finiteness of Ψ(t, k) when t and k satisfy certain conditions. The exact determination of Ψ(t, k) for specified t and k is a hard problem and only Ψ(2, 3), Ψ(2, 4), Ψ(3, 4), Ψ(4, 5), and Ψ(5, 6) have been determined. In this paper, we determin...
متن کاملAn application of graphical enumeration to PA*
For α less than ε0 let Nα be the number of occurrences of ω in the Cantor normal form of α. Further let |n| denote the binary length of a natural number n, let |n|h denote the h-times iterated binary length of n and let inv(n) be the least h such that |n|h ≤ 2. We show that for any natural number h first order Peano arithmetic, PA, does not prove the following sentence: For all K there exists a...
متن کاملEnumeration of 2-(12, 3, 2) designs
A backtrack search with isomorph rejection is carried out to enumerate the 2-(12,3,2) designs. There are 242 995 846 such designs, which have automorphism groups whose size range from 1 to 1536. There are 88 616 310 simple designs. The number of resolvable designs is 62 929; these have 74 700 nonisomorphic resolutions. We use the following standard notations. A t-(v, k, >.) design is a family o...
متن کاملEnumeration of t-Designs Through Intersection Matrices
In this paper, we exploit some intersection matrices to empower a backtracking approach based on Kramer–Mesner matrices. As an application, we consider the interesting family of simple t-ðtþ 8; tþ 2; 4Þ designs, 1 t 4, and provide a complete classification for t 1⁄4 1; 4, as well as a classification of all non-rigid designs for t 1⁄4 2; 3. We also enumerate all rigid designs for t 1⁄4 2. The co...
متن کاملAn improved finiteness theorem for graphical t-designs
We prove that there exist only "nitely many nontrivial graphical t-(v; k; ) designs when k 6 4t=3. This improves a previous result of Betten et al. (Discrete Math. 197/198 (1999) 83–109). c © 2001 Elsevier Science B.V. All rights reserved. We use the notation and terminology of [1] and assume that the reader is familiar with the concept of graphical t-designs [2]. All polynomials in this note a...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Designs
سال: 2007
ISSN: 1063-8539,1520-6610
DOI: 10.1002/jcd.20137