The extended equation of Lyndon and Sch?tzenberger
The extended equation of Lyndon and Sch?tzenberger
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Lyndon 和 Sch?tzenberger 的扩展方程
DOI：
10.1016/j.jcss.2016.11.003
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发表时间：
2017
影响因子：
1.1
通讯作者：
Seki Shinnosuke
中科院分区：
文献类型：
--
作者：
Manea Florin;M?ller Mike;Nowotka Dirk;Seki Shinnosuke
Lyndon和Schützenberger(1962)[3]研究了对于ℓ、m和n的值，字方程uℓ=v m wn只有周期解。根据他们的结果，我们精确地确定了广义ℓ-Schützenberger字方程u 1⋯uℓ=v 1⋯v m w 1⋯wn的值，其中u i∈{u，θ(U)}对于所有1≤i≤ℓ，v j∈{v，θ(V)}对于所有1≤j≤m，w k∈{w，θ(W)}对于所有1≤k≤n，并且θ是反同形对合，只有θ周期解，即，u，v，w∈{t，θ(T)}⁎表示某个单词t。这完全回答了Czeizler等人(2009年)[22]提出的一个公开问题。
Lyndon and Schützenberger (1962)[3] investigated for which values of ℓ, m, and n, the word-equations u ℓ= v m w n have only periodic solutions. Following their result, we determine precisely the values of ℓ, m, and n for which the generalised Lyndon–Schützenberger word equations u 1⋯ u ℓ= v 1⋯ v m w 1⋯ w n, where u i∈{u, θ (u)} for all 1≤ i≤ ℓ, v j∈{v, θ (v)} for all 1≤ j≤ m, w k∈{w, θ (w)} for all 1≤ k≤ n, and θ is an antimorphic involution, have only θ-periodic solutions, ie, u, v, w∈{t, θ (t)}⁎ for some word t. This answers completely an open problem by Czeizler et al.(2009)[22].