On a problem in combinatorial geometry

A combinatorial problem in geometry

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On a Problem in Combinatorial Geometry P . Erd ®

On a Combinatorial Problem

Let M be a set and F a family of its subsets. F is said by E. W. MILLER [5] to possess property B if there exists a subset K of M so that no set of the family F is contained either in K or in K (K is the complement of K in M) . HAJNAL and 1 [2] recently published a paper on the property B and its generalisations . One of the unsolved problems we state asks : What is the smallest integer in (n) ...

On a Combinatorial Problem in Latin Squares

1. Denote by S, an arbitrary latin square with n elements {a 1 , a 2 , . . . , a„ } . A row and column of this square, intersecting on the main diagonal (i .e . diagonal beginning at the left lower corner) will be called corresponding . After striking out n c arbitrary rows and corresponding columns, a square T, with c x c entries remains . Such a square will be called a principal minor. It is ...

On a Combinatorial Problem in Number Theory

1. Introduction One of the problems mentioned injl] (on p. 187) concerns the estimation of the magnitude of the largest number g(N) such that, from every sequence of N distinct natural numbers, one can always select a subsequence of g{N) integers with the property that no sum of two distinct integers of this subsequence belongs to the original sequence. It should be mentioned that the function ...