5 research outputs found
On the complexity of finding and counting solution-free sets of integers
Given a linear equation , a set of integers is
-free if does not contain any `non-trivial' solutions to
. This notion incorporates many central topics in combinatorial
number theory such as sum-free and progression-free sets. In this paper we
initiate the study of (parameterised) complexity questions involving
-free sets of integers. The main questions we consider involve
deciding whether a finite set of integers has an -free subset
of a given size, and counting all such -free subsets. We also
raise a number of open problems.Comment: 27 page
On sum-free subsets of abelian groups
In this paper we discuss some of the key properties of sum-free subsets of
abelian groups. Our discussion has been designed with a broader readership in
mind, and is hence not overly technical. We consider answers to questions like:
how many sum-free subsets are there in a given abelian group ? what are its
sum-free subsets of maximum cardinality? what is the maximum cardinality of
these sum-free subsets? what does a typical sum-free subset of looks like?
among others
On Sum-Free Subsets of Abelian Groups
In this paper, we discuss some of the key properties of sum-free subsets of abelian groups. Our discussion has been designed with a broader readership in mind and is hence not overly technical. We consider answers to questions like the following: How many sum-free subsets are there in a given abelian group G? What are its sum-free subsets of maximum cardinality? What is the maximum cardinality of these sum-free subsets? What does a typical sum-free subset of G look like
Errata and Addenda to Mathematical Constants
We humbly and briefly offer corrections and supplements to Mathematical
Constants (2003) and Mathematical Constants II (2019), both published by
Cambridge University Press. Comments are always welcome.Comment: 162 page