AbstractWe present an elementary proof of a transfinite symmetric form of Philip Hall's theorem on systems of distinct representatives and derive some wellknown mapping theorems from it to illustrate the ease with which this form of the theorem may be used
PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.li...
AbstractA family of s subsets of a finite set R is a partitioning family of R if the subsets are pai...
Let X be a finite or countable set and μ a measure on X with μ(X) = 1. Using Hall's theorem on disti...
AbstractA sufficient condition for the existence of a system of distinct representatives for a famil...
Abstract. A transversal generated by a system of distinct representatives (SDR) for a collection of ...
AbstractLet I be a finite index set and let A denote the family (Ai : i ∈ I) of finite subsets of S....
AbstractLet M = (S, I) be a matroid of finite character on the infinite set S. Let A = 〈A1:i ∈ I〉 be...
AbstractIn the present paper we investigate properties of a general notion of independence and we us...
AbstractLet U be a family of sets having a finite number of infinte members. A proof is given for a ...
AbstractI show how a reduction principle technique used by Rado [11] in his very short elegant proof...
In this note we show by a simple direct proof that Folkman's necessary and sufficient condition for ...
summary:The aim of this paper is to generalize several basic results from transversal theory, primar...
AbstractThis paper proves a conjecture of C. St. J. A. Nash-Williams giving necessary and sufficient...
summary:The theorem of Edmonds and Fulkerson states that the partial transversals of a finite family...
AbstractWe prove the following result and transfinite extensions of it: Let (Mi:i ϵ I) be a family o...
PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.li...
AbstractA family of s subsets of a finite set R is a partitioning family of R if the subsets are pai...
Let X be a finite or countable set and μ a measure on X with μ(X) = 1. Using Hall's theorem on disti...
AbstractA sufficient condition for the existence of a system of distinct representatives for a famil...
Abstract. A transversal generated by a system of distinct representatives (SDR) for a collection of ...
AbstractLet I be a finite index set and let A denote the family (Ai : i ∈ I) of finite subsets of S....
AbstractLet M = (S, I) be a matroid of finite character on the infinite set S. Let A = 〈A1:i ∈ I〉 be...
AbstractIn the present paper we investigate properties of a general notion of independence and we us...
AbstractLet U be a family of sets having a finite number of infinte members. A proof is given for a ...
AbstractI show how a reduction principle technique used by Rado [11] in his very short elegant proof...
In this note we show by a simple direct proof that Folkman's necessary and sufficient condition for ...
summary:The aim of this paper is to generalize several basic results from transversal theory, primar...
AbstractThis paper proves a conjecture of C. St. J. A. Nash-Williams giving necessary and sufficient...
summary:The theorem of Edmonds and Fulkerson states that the partial transversals of a finite family...
AbstractWe prove the following result and transfinite extensions of it: Let (Mi:i ϵ I) be a family o...
PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.li...
AbstractA family of s subsets of a finite set R is a partitioning family of R if the subsets are pai...
Let X be a finite or countable set and μ a measure on X with μ(X) = 1. Using Hall's theorem on disti...
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