A175769 Maximum cardinality of isosceles sets in E^n.

3, 6, 8, 11, 17, 28, 30, 45

Offset

1,1

Comments

An isosceles set is a set of points in a plane or in space, any three of which form an isosceles triangle.

In his 1946 problem Erdős notes that a(2) = 6 and asks for the value of a(3); L. M. Kelly proves that a(2) = 6 and shows that a(3) >= 9. The editors note that Kelly disproves a conjecture of Coxeter. - Charles R Greathouse IV, May 21 2021

Links

Table of n, a(n) for n=1..8.

Paul Erdős, Problems for Solution: E735, The American Mathematical Monthly, vol. 53, no. 7 (August 1946), p. 394.

Paul Erdős and L. M. Kelly, Isosceles n-points, The American Mathematical Monthly, vol. 54, no. 4 (April 1947), pp. 227-229.

Yury J. Ionin, Isosceles Sets, The Electronic Journal of Combinatorics, Vol. 16, No. 1 (2009), R141.

Crossrefs

Cf. A027627.

Sequence in context: A360532 A289241 A234307 * A352211 A160277 A080598

Adjacent sequences: A175766 A175767 A175768 * A175770 A175771 A175772

Keyword

nonn,more,hard

Author

John W. Layman, Sep 01 2010

Extensions

Comment corrected by John W. Layman, Sep 03 2010

Status

approved