Sequences with long range exclusions

Details Sequences with long range exclusions Sequences with long range exclusions

2012-04-16

arxiv.org/abs/1204.3439v1

Mathematics

Probability

13 pages

Scientific paper

Given a finite alphabet $S$, we study subsets of the full sequence space $S^{\rm {\bf Z}}$ given by the additional restriction that $x_i\not=x_{i+f(n)},\ i\in {\rm {\bf Z}},\ n\in {\rm {\bf N}}.$ Here $f$ is a positive, strictly increasing function. Of particular interest is the case $f(n)=n^2$, a problem originally proposed by M. Keane. There our analysis proceeds via a probabilistic model involving a special kind of RWRE. For most $f$ that we consider we will see that the resulting spaces are very small, even for arbitrarily large $S$.

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