منابع مشابه
Asymptotic existence theorems for frames and group divisible designs
In this paper, we establish an asymptotic existence theorem for group divisible designs of type mn with block sizes in any given set K of integers greater than 1. As consequences, we will prove an asymptotic existence theorem for frames and derive a partial asymptotic existence theorem for resolvable group divisible designs. © 2006 Elsevier Inc. All rights reserved.
متن کاملOn Matroid Theorems of Edmonds and Rado
Introduction In this note I show how very general and powerful results about the union and intersection of matroids due to J. Edmonds [19] may be deduced from a matroid generalisation of Hall's theorem by R. Rado [13]. Throughout, S, T, will denote finite sets, |X| will denote the cardinality of the set X and {xt: iel} denotes the set whose distinct elements are the elements x{. A matroid (S, M...
متن کاملExistence Theorems for Warfield Groups
Warfield studied p-local groups that are summands of simply presented groups, introducing invariants that, together with Ulm invariants, determine these groups up to isomorphism. In this paper, necessary and sufficient conditions are given for the existence of a Warfield group with prescribed Ulm and Warfield invariants. It is shown that every Warfield group is the direct sum of a simply presen...
متن کاملAn Existence Theory for Pairwise Balanced Designs I. Composition Theorems and Morphisms
One of the most central problems of modern combinatorial theory is the determination of those parameter triples (v, k, X) for which there exist (0, k, h)-BIBD’s (balanced incomplete block designs). The methods which have been put forth to construct BIBD’s divide roughly into two classes: direct constructions where a BIBD is obtained from an algebraic structure (often a design is constructed fro...
متن کاملSome Properties of Perfect Matroid Designs
Blocks of a matroid are called hyperplanes. For various definitions and results connected with matroids, see [26]. Subsets of X , which are intersections of hyperplanes are called flats of a matroid. Each subset Y c_ X has a well-defined rank. If F is a flat of rank i and x e X \ F , then, there is a unique flat of rank (i + 1) which contains FU{x}. Rank of X is said to be the rank of matroid. ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1973
ISSN: 0002-9947
DOI: 10.2307/1996457