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A theorem on cubes
Author(s) -
Woodall D. R.
Publication year - 1977
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300008913
Subject(s) - mathematics , combinatorics , cube (algebra) , set (abstract data type) , line (geometry) , discrete mathematics , geometry , computer science , programming language
Summary It is proved that, if R is a set of r vertices of an n –dimensional cube, then the number of distinct mid‐points of line‐segments joining pairs of points of R (including the points of R themselves as mid‐points) is at least r x , where ∝ = log 3 / log 2.This result is (in a sense) best possible.