English

Avoidability of circular formulas

Discrete Mathematics 2016-10-17 v1

Abstract

Clark has defined the notion of nn-avoidance basis which contains the avoidable formulas with at most nn variables that are closest to be unavoidable in some sense. The family CiC_i of circular formulas is such that C1=AAC_1=AA, C2=ABA.BABC_2=ABA.BAB, C3=ABCA.BCAB.CABCC_3=ABCA.BCAB.CABC and so on. For every ini\le n, the nn-avoidance basis contains CiC_i. Clark showed that the avoidability index of every circular formula and of every formula in the 33-avoidance basis (and thus of every avoidable formula containing at most 3 variables) is at most 4. We determine exactly the avoidability index of these formulas.

Cite

@article{arxiv.1610.04439,
  title  = {Avoidability of circular formulas},
  author = {Guilhem Gamard and Pascal Ochem and Gwenaël Richomme and Patrice Séébold},
  journal= {arXiv preprint arXiv:1610.04439},
  year   = {2016}
}
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