2014
DOI: 10.1007/s11464-014-0379-1
|View full text |Cite
|
Sign up to set email alerts
|

Relative locations of subwords in free operated semigroups and Motzkin words

Abstract: 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 applyin… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1

Citation Types

0
11
0

Year Published

2015
2015
2018
2018

Publication Types

Select...
5

Relationship

3
2

Authors

Journals

citations
Cited by 7 publications
(11 citation statements)
references
References 14 publications
0
11
0
Order By: Relevance
“…we have kR(∆X) kM {P} (∆X)/J RB kM {P,d} (X)/J DRB . By [24,Theorem 4.11], the statement of the present theorem holds when R n is replaced by M {P} (∆X). Since R(∆X) and hence R n are subsets of M {P} (∆X), the statement of the theorem remains true for R(∆X) and R n .…”
Section: Definition 42mentioning
confidence: 93%
See 2 more Smart Citations
“…we have kR(∆X) kM {P} (∆X)/J RB kM {P,d} (X)/J DRB . By [24,Theorem 4.11], the statement of the present theorem holds when R n is replaced by M {P} (∆X). Since R(∆X) and hence R n are subsets of M {P} (∆X), the statement of the theorem remains true for R(∆X) and R n .…”
Section: Definition 42mentioning
confidence: 93%
“…For the purpose of the proof the next lemma, we describe the relative location of two bracketed subwords in the more precise notion of placements (or occurrences [10]) in a bracketed word. See [24] for details. But note that we focus on words in R n as a subset of M(∆ n X).…”
Section: Definition 42mentioning
confidence: 99%
See 1 more Smart Citation
“…The following concept is finer than bracketed subwords, containing the information of placements [29]. Definition 3.4.…”
Section: Applicationsmentioning
confidence: 99%
“…From the definition of n for n 0, we see that the restriction of the order n+1 to M n (Z) equals to the order n . Thus we can define the order (43) db := lim…”
mentioning
confidence: 99%