Further results on irregular, critical perfect systems of difference sets II: systems without splits
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TLDR
A general method of construction is described and used to show that there are such systems for 2⩽ n ⩽4 and certain values of c depending on n and the limitations of this method are discussed.About:
This article is published in Discrete Mathematics.The article was published on 1992-12-11 and is currently open access. It has received 3 citations till now. The article focuses on the topics: Valency.read more
Citations
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Book ChapterDOI
Critical Perfect Systems of Difference Sets
TL;DR: In this paper, the authors describe critical perfect systems of difference triangles, where the sum of entries in the kth row from the apex of a triangle is equal to the sum in the first row of the triangle from the bottom.
Journal ArticleDOI
On critical perfect systems of difference sets
TL;DR: It is shown that a critical perfect system of difference sets with threshold c which contains no difference sets of valency 2 consists of 2c - 1 difference setsof valency 3.
Journal ArticleDOI
Further results on irregular, critical perfect systems of difference sets I: split systems
G. M. Hamilton,D. G. Rogers +1 more
TL;DR: It is shown that, for some c and n, there are (2c − 1, n; 3, 6; c)-systems which have a certain splitting property enabling them to be pulled apart nicely and the bearing of these results on the study of critical perfect systems and on the multiplication theorem for these systems is discussed.
References
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Journal ArticleDOI
Irregular Extremal Perfect Systems of Difference Sets
TL;DR: Theoremes d'existence des systemes parfaits extremaux irreguliers d'ensembles de differences as mentioned in this paper, i.e., systems that are irreguleurs of differences
Journal ArticleDOI
An arithmetic of complete permutations with constraints, 1: an exposition of the general theory
TL;DR: An arithmetic of complete permutations of symmetric, integral bases is developed, comparable to that of perfect systems of difference sets with which there are several interrelations, and super-position of permutations provides the addition of this arithmetic.
Journal ArticleDOI
An arithmetic of complete permutations with constraints, II: case studies
D. J. Crampin,D. G. Rogers +1 more
TL;DR: Using the arithmetic of complete permutations developed in the first part of this paper, the spectra of certain constraints with respect to central, integral bases which are of interest are investigated for the purposes of giving further constructions either ofcomplete permutations with constraints or of irregular, critical perfect systems of difference sets.
Journal ArticleDOI
On the general Erdo¨s conjecture for perfect systems of difference sets and embedding partial complete permutation
TL;DR: The (general) Erdos conjecture for perfect systems of difference sets is confirmed; namely that, for each threshold c ⩾ 1, all sufficiently long finite runs of consecutive integers beginning with c can be partitioned into such systems.
Journal ArticleDOI
Irregular, extremal perfect systems of difference sets II
TL;DR: It is shown here that if there is a (2c − 1,n; u, 6;c)-system thenn = 0 whenu = 4 andn ≤ 2c −1 when u = 3, this last result being of possible interest in connection with the multiplication theorem for perfect systems.