New York Journal of Mathematics
Volume 13 (2007) 97-106


Neil Hindman and Henry Jordan

Measures of sum-free intersecting families

Published: March 24, 2007
Keywords: Sum-free, maximal sum-free, intersecting families
Subject: Primary 28A12; Secondary 05A15, 11B75, 05D10

Let α be the supremum of all δ such that there is a sequence <An>n=1 of measurable subsets of (0,1) with the property that each An has measure at least δ and for all n,m∈N, An∩ Am∩ An+m=∅. For k∈N, let αk be the corresponding supremum for finite sequences <An>n=1k. We show that α=limk→∞αk and find the exact value of αk for k≦41. In the process of finding these exact values, we also determine exactly the number of maximal sum free subsets of {1,2,...,k} for k≦41. We also investigate the size of sets <Ax>x∈S with Ax∩ Ay∩ Ax+y=∅ where S is a subsemigroup of ((0,∞),+).


The first author acknowledges support recieved from the National Science Foundation via Grant DMS-0554803

Author information

Department of Mathematics, Howard University, Washington, DC 20059