$A_n$和$\widetilde{A}_n$型Hecke-Kiselman幺半群的字问题
The word problem for Hecke--Kiselman monoids of type $A_n$ and $\widetilde{A}_n$
摘要：
我们表现出明确的和容易实现的双射之间的Hecke-Kiselman幺半群的类型$A_n$/$\widetilde{A}_n$;某些编织图的平面/圆柱;和夫妇的整数序列的特定类型。这产生了一个快速的解决方案的字问题和一个有效的正规形式，这些香港幺半群。杨-巴克斯特型行动在我们的建设中起着重要的作用。
英文摘要：
We exhibit explicit and easily realisable bijections between Hecke--Kiselman monoids of type $A_n$/$\widetilde{A}_n$; certain braid diagrams on the plane/cylinder; and couples of integer sequences of particular types. This yields a fast solution of the word problem and an efficient normal form for these HK monoids. Yang--Baxter type actions play an important role in our constructions.
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。
