منابع مشابه
Some Pairwise Balanced Designs
A pairwise balanced design, B(K; v), is a block design on v points, with block sizes taken from K, and with every pair of points occurring in a unique block; for a fixed K, B(K) is the set of all v for which a B(K; v) exists. A set, S, is a PBD-basis for the set, T , if T = B(S). Let Na(m) = {n : n ≡ a mod m}, and N≥m = {n : n ≥ m}; with Q the corresponding restriction of N to prime powers. Thi...
متن کاملPairwise balanced designs and sigma clique partitions
In this paper, we are interested inminimizing the sum of block sizes in a pairwise balanced design, where there are some constraints on the size of one block or the size of the largest block. For every positive integers n,m, wherem ≤ n, letS (n,m) be the smallest integer s for which there exists a PBD on n points whose largest block has sizem and the sum of its block sizes is equal to s. Also, ...
متن کاملPairwise balanced designs of dimension three
The dimension of a pairwise balanced design PBD(v,K) is the maximum positive integer d such that any d of its points are contained in a proper flat. The standard examples are affine and projective linear spaces. Also, Teirlinck provided a nearly complete existence theory for ‘Steiner spaces’, which is the case K = {3} and d = 3. A recent result of the first author and A.C.H. Ling says that ther...
متن کاملExtremal Problems 2or Pairwise Balanced Designs
1 . Introduction In a previous paper [2] the senior author discussed many problems concerning block designs . Some of these have since been settled . Szemerédi and Trotter [5] showed, for example, that the number of pairwise balanced designs which can be obtained geometrically on n points in the plane with the blocks being the lines joining these points is at most exp(c/) . In [1] Colbourn, Phe...
متن کاملPairwise balanced designs from nite elds
Developing previous work by R.C. Bose, R.M. Wilson, M. Greig and the author, we give a general construction for di erence families over nite elds. All the DFs constructed before were generated by a single initial base block so that they were uniform. Here we also consider DFs generated by two or more initial base blocks. These DFs give rise to pairwise balanced designs which of course are balan...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1999
ISSN: 1077-8926
DOI: 10.37236/1491