TY - JOUR
A2 - Rodger, Chris A.
AU - Eggleton, Roger B.
PY - 2014
DA - 2014/08/26
TI - Midpoint-Free Subsets of the Real Numbers
SP - 214637
VL - 2014
AB - A set of reals S⊂R is midpoint-free if it has no subset a, b, c⊆S such that a<b<c and a+c=2b. If S⊂X⊆R and S is midpoint-free, it is a maximal midpoint-free subset of X if there is no midpoint-free set T such that S⊂T⊆X. In each of the cases X=Z+, Z, Q+,Q,R+,R, we determine two maximal midpoint-free subsets of X characterised by digit constraints on the base 3 representations of their members.
SN - 1687-9163
UR - https://doi.org/10.1155/2014/214637
DO - 10.1155/2014/214637
JF - International Journal of Combinatorics
PB - Hindawi Publishing Corporation
KW -
ER -