Showing papers in "American Mathematical Monthly in 1964"
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TL;DR: The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming.
3,478 citations
912 citations
910 citations
686 citations
TL;DR: The number of partitions of a set has been studied in the context of the number of partitions of sets as mentioned in this paper, and it is shown to be a function of the size of the set.
Abstract: (1964). The Number of Partitions of a Set. The American Mathematical Monthly: Vol. 71, No. 5, pp. 498-504.
462 citations
372 citations
301 citations
TL;DR: Inverse Relations and Combinatorial Identities: Inverse relations and combinatorial identities as mentioned in this paper are a generalization of the notion of Inverse Relations in algebraic geometry.
Abstract: (1964). Inverse Relations and Combinatorial Identities. The American Mathematical Monthly: Vol. 71, No. 5, pp. 485-498.
286 citations
TL;DR: In this article, it is shown that with the addition of any new edge a compIete k-graph is formed, where each edge joins a vertex to itself and at most one edge joins any two vertices.
Abstract: A gruph consists of a finite set of vertices some pairs of which are adjacent, i.e., joined by an edge. No edge joins a vertex to itself and at most one edge joins any two vertices. The degree of a vertex is the number of vertices adjacent to it. The complete k-graph has k vertices and @ edges. We shall say that a graph G has property (n, k), where n and k are integers with 25 kSn, if G has n vertices and the addition of any new edge increases the number of complete k-graphs contained in G. For example, let Ar{n) denote a graph with n vertices and n(k-2)-(',I) edges which consist of a complete (k-2)-graph each vertex of which is also joined to each of the n-(k-2) remaining vertices. A&z) contains no complete k-graphs but it is easily seen that with the addition of any new edge a compIete k-graph is formed. Hence, &(n) has property b, k).
269 citations
TL;DR: In this paper, the classification of symmetric spaces has been studied in the context of Lie groups and Lie algebras, and a list of notational conventions has been proposed.
Abstract: Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type Symmetric spaces of the compact type Hermitian symmetric spaces On the classification of symmetric spaces Functions on symmetric spaces Bibliography List of notational conventions Symbols frequently used Author index Subject index Reviews for the first edition.
TL;DR: A Periodic Optimal Search (POS) as mentioned in this paper is a periodic optimal search algorithm for the periodic search problem with the objective of minimizing the number of iterations of the optimal search.
Abstract: (1964). A Periodic Optimal Search. The American Mathematical Monthly: Vol. 71, No. 1, pp. 15-21.
TL;DR: The Product of Separable Spaces (POS) as discussed by the authors is a collection of products of separable spaces that can be used to define separable space classes in the mathematical domain.
Abstract: (1964). Products of Separable Spaces. The American Mathematical Monthly: Vol. 71, No. 4, pp. 398-403.
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