 

Neil Hindman and Henry Jordan
Measures of sumfree intersecting families


Published: 
March 24, 2007

Keywords: 
Sumfree, maximal sumfree, intersecting families 
Subject: 
Primary 28A12; Secondary 05A15, 11B75, 05D10 


Abstract
Let α be the supremum of all δ such that
there is a sequence <A_{n}>_{n=1}^{∞} of measurable
subsets of (0,1) with the property that each A_{n} has measure
at least δ and for all n,m∈N, A_{n}∩ A_{m}∩
A_{n+m}=∅. For k∈N, let α_{k} be the
corresponding supremum for finite sequences <A_{n}>_{n=1}^{k}.
We show that α=lim_{k→∞}α_{k} and
find the exact value of α_{k} 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 <A_{x}>_{x∈S} with
A_{x}∩ A_{y}∩ A_{x+y}=∅ where S is a subsemigroup of
((0,∞),+).


Acknowledgements
The first author acknowledges support recieved from the National Science Foundation via Grant DMS0554803


Author information
Department of Mathematics, Howard University, Washington, DC 20059
nhindman@aol.com
http://members.aol.com/nhindman
henryjordan59@hotmail.com

