منابع مشابه
Stapled Sequences and Stapling Coverings of Natural Numbers
A stapled sequence is a set of consecutive positive integers such that no one of them is relatively prime with all of the others. The problem of existence and construction of stapled sequences of length N was extensively studied for over 60 years by Pillai, Evans, Brauer, Harborth, Erdös and others. Sivasankaranarayana, Szekeres and Pillai proved that no stapled sequences exist for any N < 17. ...
متن کاملOn category of co-coverings
In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.
متن کاملFractional Coverings, Greedy Coverings, and Rectifier Networks
A rectifier network is a directed acyclic graph with distinguished sources and sinks; it is said to compute a Boolean matrix M that has a 1 in the entry (i, j) iff there is a path from the jth source to the ith sink. The smallest number of edges in a rectifier network that computes M is a classic complexity measure on matrices, which has been studied for more than half a century. We explore two...
متن کاملUniversal Cycles for Minimum Coverings of Pairs by Triples, with Application to 2-Radius Sequences
A new ordering, extending the notion of universal cycles of Chung et al. (1992), is proposed for the blocks of k-uniform set systems. Existence of minimum coverings of pairs by triples that possess such an ordering is established for all orders. The application to the construction of short 2-radius sequences is given, along with some new 2-radius sequences found through a computer search.
متن کاملThin Coverings of Modules
Thin coverings are a method of constructing graded-simple modules from simple (ungraded) modules. After a general discussion, we classify the thin coverings of (quasifinite) simple modules over associative algebras graded by finite abelian groups. The classification uses the representation theory of cyclotomic quantum tori. We close with an application to representations of multiloop Lie algebras.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1960
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1960.10.689