English

A squarefree term not occurring in the Leech sequence

Combinatorics 2020-03-30 v1 Discrete Mathematics

Abstract

Let A=ABCBA CBC ABCBA,B=BCACB ACA BCACB,C=CABAC BAB CABAC. \begin{array}{c}\overline{A} = ABCBA\ CBC\ ABCBA,\\ \overline{B} = BCACB\ ACA\ BCACB,\\ \overline{C} = CABAC\ BAB\ CABAC. \end{array} The Leech sequence LL is the squarefree sequence obtained as the limit of the palindromes A,A,A,. A, \overline{A}, \overline{\overline{A}}, \ldots . In order to specify a certain class of pseudorecursive varieties of semigroups, it is helpful to have a squarefree term in 3 variables such that no substitution instance occurs as a subterm of LL. We show that κ1=aba cbc aba c\kappa_1 = aba\ cbc\ aba\ c is such a term. Except for one situation, the doubly-linked term κ2=aba cbc aba\kappa_2 = aba\ cbc\ aba will serve, and we focus on it.

Cite

@article{arxiv.2003.12213,
  title  = {A squarefree term not occurring in the Leech sequence},
  author = {Benjamin Wells},
  journal= {arXiv preprint arXiv:2003.12213},
  year   = {2020}
}

Comments

22 pages

R2 v1 2026-06-23T14:28:49.777Z