On factor-free Dyck words with half-integer slope
| Autor: | Juan B. Gil, Daniel Birmajer, Michael D. Weiner |
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| Rok vydání: | 2018 |
| Předmět: |
Class (set theory)
0102 computer and information sciences 02 engineering and technology 01 natural sciences Bell polynomials Combinatorics Corollary Factor (programming language) 0202 electrical engineering electronic engineering information engineering Enumeration FOS: Mathematics Mathematics - Combinatorics Algebraic number Mathematics computer.programming_language Mathematics::Combinatorics Applied Mathematics 020206 networking & telecommunications Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Lattice path 010201 computation theory & mathematics Half-integer Combinatorics (math.CO) 05A15 computer Computer Science::Formal Languages and Automata Theory |
| DOI: | 10.48550/arxiv.1804.11244 |
| Popis: | We study a class of rational Dyck paths with slope (2m+1)/2 corresponding to factor-free Dyck words, as introduced by P. Duchon. We show that, for the slopes considered in this paper, the language of factor-free Dyck words is generated by an auxiliary language that we examine from the algebraic and combinatorial points of view. We provide a lattice path description of this language, and give an explicit enumeration formula in terms of partial Bell polynomials. As a corollary, we obtain new formulas for the number of associated factor-free generalized Dyck words. Comment: 13 pages. To appear in Advances in Applied Mathematics |
| Databáze: | OpenAIRE |
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