Relative locations of operated semigroups subwords in free and Motzkin words  

作　　者：Shanghua ZHENG LI GUO 

机构地区：[1]Department of Mathematics, Lanzhou University, Lanzhou 730000, China [2]Department of Mathematics'and Computer Science, Rutgers University, Newark, NJ 07102, USA

出　　处：《Frontiers of Mathematics in China》2015年第5期1243-1261,共19页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements The authors thank the Kavli Institute for Theoretical Physics China and the Morningside Center for Mathematics in Beijing for their hospitality and support. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11201201, 11371178）, the Fundamental Research Funds for the Central Universities （lzujbky-2013-8）, and the National Science Foundation of US （Grant No. DMS 1001855）.

摘　　要：Bracketed words are basic structures both in mathematics （such as Rota-Baxter algebras） and mathematical physics （such as rooted trees） where the locations of the substructures are important. In this paper, we give the classification of the relative locations of two bracketed subwords of a bracketed word in an operated semigroup into the separated, nested, and intersecting cases. We achieve this by establishing a correspondence between relative locations of bracketed words and those of words by applying the concept of Motzkin words which are the algebraic forms of Motzkin paths.Bracketed words are basic structures both in mathematics （such as Rota-Baxter algebras） and mathematical physics （such as rooted trees） where the locations of the substructures are important. In this paper, we give the classification of the relative locations of two bracketed subwords of a bracketed word in an operated semigroup into the separated, nested, and intersecting cases. We achieve this by establishing a correspondence between relative locations of bracketed words and those of words by applying the concept of Motzkin words which are the algebraic forms of Motzkin paths.

关 键 词：Bracketed word relative location operated semigroup Motzkinword Motzkin path rooted tree 

分 类 号：O175.12[理学—数学] N031[理学—基础数学]