论文标题

在水ech序列中不存在的无方术语

A squarefree term not occurring in the Leech sequence

论文作者

Wells, Benjamin

论文摘要

Let \[ \begin{array}{c}\overline{A} = ABCBA\ CBC\ ABCBA,\\ \overline{B} = BCACB\ ACA\ BCACB,\\ \overline{C} = CABAC\ BAB\ CABAC. \ end {array} \] leech序列$ l $是作为palindromes \ [a,\ overline {a},\ overline {\ overline {\ overline {a}},\ ldots获得的平方序列。 \]为了指定一定类别的Semigroups的伪经销品种,在3个变量中拥有一个无方术语是有帮助的,因此没有替换实例作为$ l $的替代实例。我们表明$κ__1= aba \ cbc \ aba \ c $是这样的术语。除一种情况外,双连锁项$κ_2= aba \ cbc \ aba $将使用,我们将重点放在上面。

Let \[ \begin{array}{c}\overline{A} = ABCBA\ CBC\ ABCBA,\\ \overline{B} = BCACB\ ACA\ BCACB,\\ \overline{C} = CABAC\ BAB\ CABAC. \end{array} \] The Leech sequence $L$ is the squarefree sequence obtained as the limit of the palindromes \[ A, \overline{A}, \overline{\overline{A}}, \ldots . \] 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 $L$. We show that $κ_1 = aba\ cbc\ aba\ c$ is such a term. Except for one situation, the doubly-linked term $κ_2 = aba\ cbc\ aba$ will serve, and we focus on it.

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