A presentation of a finitely generated submonoid of invertible endomorphisms of the free monoid
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- 作者：Christian Choffrut ; Štěpán Holub
- 关键词：Invertible substitutions ; Nielsen transformation ; Monoid presentation
- 刊名：Semigroup Forum
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：93
- 期：3
- 页码：444-458
- 全文大小：460 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics<br>Algebra<br>
- 出版者：Springer New York
- ISSN：1432-2137
- 卷排序：93
文摘
An endomorphism of the free monoid \({A}^*\) is invertible if it is injective and extends to an automorphism of the free group generated by \({A}\). A simple example: the endomorphism that leaves all generators \({A}\) invariant except one, say a, which is mapped to ba for some other generator b. We give a monoid presentation for the submonoid generated by all such endomorphisms when a and b are taken arbitrarily. These left translations are a special case of Nielsen positive transformations: “left” because the mutiplicative constant acts on the left and “positive” because this constant belongs to the free monoid, not the free group.