Stalactic，Taiga，Sylvester和Baxter幺半群的有限基问题
Finite basis problems for stalactic, taiga, sylvester and Baxter monoids
摘要：
Stalactic、Taiga、Sylvester和Baxter幺半群都是从组合学的tableaux中产生的，只要它们通过某种插入算法产生相同的tableaux，它们就可以在一个固定的有序字母表上识别单词。本文给出了半群是单基半群的三个充分条件。通过应用这些充分条件，证明了所有秩大于或等于$2$的stalactic幺半群和taiga幺半群都是基于矩阵的且满足相同的恒等式，所有秩大于或等于$2$的sylvester幺半群都是基于矩阵的且满足相同的恒等式，所有秩大于或等于$2$的Baxter幺半群都是基于矩阵的且满足相同的恒等式.
英文摘要：
Stalactic, taiga, sylvester and Baxter monoids arise from the combinatorics of tableaux by identifying words over a fixed ordered alphabet whenever they produce the same tableau via some insertion algorithm. In this paper, three sufficient conditions under which semigroups are finitely based are given. By applying these sufficient conditions, it is shown that all stalactic and taiga monoids of rank greater than or equal to $2$ are finitely based and satisfy the same identities, that all sylvester monoids of rank greater than or equal to $2$ are finitely based and satisfy the same identities and that all Baxter monoids of rank greater than or equal to $2$ are finitely based and satisfy the same identities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
