The complexity of solution-free sets of integers for general linear equations

  title={The complexity of solution-free sets of integers for general linear equations},
  author={Keith J. Edwards and Steven D. Noble},
  journal={Discret. Appl. Math.},
Maximum k-sum n-free sets of the 2-dimensional integer lattice
For a positive integer n, let [n] denote {1, . . . , n}. For a 2-dimensional integer lattice point b and positive integers k > 2 and n, a k-sum b-free set of [n] × [n] is a subset S of [n] × [n] such
Maximum $k$-Sum $\mathbf{n}$-Free Sets of the 2-Dimensional Integer Lattice
The maximum density of a $k$-sum $\mathbf{b}$-free set of $[n]\times [n]$ is determined, the first investigation of the non-homogeneous sum- free set problem in higher dimensions.


On the complexity of finding and counting solution-free sets of integers
The Complexity of Enumeration and Reliability Problems
  • L. Valiant
  • Mathematics, Computer Science
    SIAM J. Comput.
  • 1979
For a large number of natural counting problems for which there was no previous indication of intractability, that they belong to the class of computationally eqivalent counting problems that are at least as difficult as the NP-complete problems.
Some Simplified NP-Complete Graph Problems
Extremal Problems in Number Theory
I would like to illustrate the problems which I shall investigate in this paper by an example. Denote by r&z) the maximum number of integers not exceeding n, no k of which form an arithmetic
Sets of integers with no large sum-free subset
Answering a question of P. Erd}os from 1965, we show that for every " > 0 there is a set A of n integers with the following property: every set A 0 A with at least 1 + " n elements contains three
Systems of distinct representatives and linear algebra
So me purposes of thi s paper are: (1) To take se riously the term , " term rank. " (2) To ma ke an issue of not " rea rra nging rows a nd colu mns" by not "a rranging" the m in the firs t place. (3)
The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected
Several enumeration and reliability problems are shown to be # P-complete, and hence, at least as hard as NP-complete problems. Included are important problems in network reliability analysis,