论文标题
在一类Monadic单相关的DEHN功能上
On the Dehn functions of a class of monadic one-relation monoids
论文作者
论文摘要
我们给出了一个无限的单体家族$π_n$（对于$ n = 2，3，\ dots $），每个都具有$ bua $ bua = a $的单个定义关系，因此$π_n$的dehn函数至少是指数。更确切地说，我们证明了$ \ partial_n（n）$ of $π_n$满足$ \ partial_n（n）\ succeq n^{n/4} $。这是Cain＆Maltcev在2013年提出的一个问题，该问题是关于$ bua = a $的单个关系所定义的每个单体是否具有二次dehn函数。最后，通过在Metabelian baumslag- s-solitar offer $ \ permatatorName {bs}（1，n）$中使用理性子集成员问题的可决定性，用于所有$ n \ geq 2 $，最近由Cadilhac，Cadilhac，Chistikov＆Zetzsche证明，我们都表明每个$ foble $。
We give an infinite family of monoids $Π_N$ (for $N=2, 3, \dots$), each with a single defining relation of the form $bUa = a$, such that the Dehn function of $Π_N$ is at least exponential. More precisely, we prove that the Dehn function $\partial_N(n)$ of $Π_N$ satisfies $\partial_N(n) \succeq N^{n/4}$. This answers negatively a question posed by Cain & Maltcev in 2013 on whether every monoid defined by a single relation of the form $bUa=a$ has quadratic Dehn function. Finally, by using the decidability of the rational subset membership problem in the metabelian Baumslag--Solitar groups $\operatorname{BS}(1,n)$ for all $n \geq 2$, proved recently by Cadilhac, Chistikov & Zetzsche, we show that each $Π_N$ has decidable word problem.
