Frontiers of Mathematics in China >
Relative locations of subwords in free operated semigroups and Motzkin words
Received date: 12 Dec 2013
Accepted date: 11 Apr 2014
Published date: 24 Jun 2015
Copyright
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.
Key words： Bracketed word; relative location; operated semigroup; Motzkin word; Motzkin path; rooted tree
Shanghua ZHENG , LI GUO . Relative locations of subwords in free operated semigroups and Motzkin words[J]. Frontiers of Mathematics in China, 2015 , 10(5) : 1243 -1261 . DOI: 10.1007/s11464-014-0379-1
| 1 |
Alonso L. Uniform generation of a Motzkin word. Theoret Comput Sci, 1994, 134: 529-536
|
| 2 |
Baader F, Nipkow T. Term Rewriting and All That. Cambridge: Cambridge Univ Press, 1998
|
| 3 |
Bogner C, Weinzierl S. Blowing up Feynman integrals. Nucl Phys B Proc Suppl, 2008, 183: 256-261
|
| 4 |
Bokut L A, Chen Y Q, Chen Y S. Composition-Diamond lemma for tensor product of free algebras. J Algebra, 2010, 323: 2520-2537
|
| 5 |
Bokut L A, Chen Y Q, Deng X, Gröbner-Shirshov bases for Rota-Baxter algebras. Sib Math J, 2010, 51: 978-988
|
| 6 |
Bokut L A, Chen Y Q, Li Y. Gröbner-Shirshov bases for categories. In: Operads and Universal Algebra. Singapore: World Scientific Press, 2012, 1-23
|
| 7 |
Bokut L A, Chen Y Q, Qiu J. Greobner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras. J Pure Appl Algebra, 2010, 214: 89-110
|
| 8 |
Buchberger B. An algorithm for finding a basis for the residue class ring of a zerodimensional polynomial ideal. Ph D Thesis, University of Innsbruck, Austria, 1965 (in German)
|
| 9 |
Connes A, Kreimer D. Hopf algebras, renormalization and concommutative geometry. Comm Math Phys, 1998, 199: 203-242
|
| 10 |
Connes A, Kreimer D. Renormalization in quantum field theory and the Riemann-Hilbert problem. I. The Hopf algebra structure of graphs and the main theorem. Comm Math Phys, 2000, 210: 249-273
|
| 11 |
Donaghey R, Shapiro L W. Motzkin numbers. J Combin Theory Ser A, 1977, 23: 291-301
|
| 12 |
Flajolet P. Mathematical methods in the analysis of algorithms and data structures. In: Trends in Theoretical Computer Science (Udine, 1984). Principles Comput Sci Ser 12. Rockville: Computer Sci Press, 1988, 225-304
|
| 13 |
Guo L. Operated semigroups, Motzkin paths and rooted trees. J Algebraic Combin, 2009, 29: 35-62
|
| 14 |
Guo L. An Introduction to Rota-Baxter Algebra. Beijing/Boston: Higher Education Press/International Press, 2012
|
| 15 |
Guo L, Sit W, Zhang R. Differential type operators and Gröbner-Shirshov bases. J Symbolic Comput, 2013, 52: 97-123
|
| 16 |
Krajewski T, Wulkenhaar R. On Kreimer’s Hopf algebra structure of Feynman graphs. Eur Phys J C, 1999, 7: 697-708
|
| 17 |
Kreimer D. On overlapping divergences. Comm Math Phys, 1999, 204: 669-689
|
| 18 |
Sapounakis A, Tsikouras P. On k-colored Motzkin words. J Integer Seq, 2004, 7: Article 04. 2.5.
|
| 19 |
Shirshov A I. Some algorithmic problem for Å-algebras. Sibirsk Mat Zh, 1962, 3: 132-137
|
| 20 |
Zheng S, Gao X, Guo L, Sit W. Rota-Baxter type operators, rewriting systems and Gröbner-Shirshov bases. Preprint
|
/
| 〈 |
|
〉 |