English

Avoiding Three Consecutive Blocks of the Same Size and Same Sum

Discrete Mathematics 2011-08-11 v3 Combinatorics

Abstract

We show that there exists an infinite word over the alphabet {0, 1, 3, 4} containing no three consecutive blocks of the same size and the same sum. This answers an open problem of Pirillo and Varricchio from 1994.

Cite

@article{arxiv.1106.5204,
  title  = {Avoiding Three Consecutive Blocks of the Same Size and Same Sum},
  author = {Julien Cassaigne and James D. Currie and Luke Schaeffer and Jeffrey Shallit},
  journal= {arXiv preprint arXiv:1106.5204},
  year   = {2011}
}
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