Relative locations of subwords in free operated semigroups and Motzkin words

doi:10.1007/s11464-014-0379-1

Front. Math. China

2015, Vol. 10

Issue (5) : 1243-1261 https://doi.org/10.1007/s11464-014-0379-1

RESEARCH ARTICLE

Relative locations of subwords in free operated semigroups and Motzkin words

Shanghua ZHENG¹,LI GUO^1,^2,^*(

)

1. Department of Mathematics, Lanzhou University, Lanzhou 730000, China
2. Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102, USA

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Abstract

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.

Keywords Bracketed word relative location operated semigroup Motzkin word Motzkin path rooted tree

Corresponding Author(s): LI GUO

Issue Date: 24 June 2015

Cite this article:

Shanghua ZHENG,LI GUO. Relative locations of subwords in free operated semigroups and Motzkin words[J]. Front. Math. China, 2015, 10(5): 1243-1261.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0379-1
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I5/1243

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