Remarks on a Problem of Moser
- 1 March 1972
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 15 (1) , 19-21
- https://doi.org/10.4153/cmb-1972-004-8
Abstract
Let M(n) be the set of all the points (x1, x2,…, xn)∈En such that xi∈{0,1,2} for each i= 1, 2,…, n and let f(n) be the cardinality of a largest subset of M(n) containing no three distinct collinear points. L. moser [4] asked for a proof of the inequality Let us consider the set Sn of those points (x1x2,…, xn)∈M(n) which satisfy |{i:Xi= 1}| = [(n +1)/3]. As Sn is a subset of the sphere with center at (1, 1,…, 1) and radius (n-[(n+1)/3])1/2, no three distinct points of Sn are collinear. Thus we have 1Keywords
This publication has 3 references indexed in Scilit:
- On sets of integers containing no four elements in arithmetic progressionActa Mathematica Hungarica, 1969
- Regularity and positional gamesTransactions of the American Mathematical Society, 1963
- On Certain Sets of IntegersJournal of the London Mathematical Society, 1953