On factor-free Dyck words with half-integer slope

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We study a class of rational Dyck paths with slope [Formula presented] 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.

Original languageEnglish (US)
Pages (from-to)94-108
Number of pages15
JournalAdvances in Applied Mathematics
Volume99
DOIs
StatePublished - Aug 1 2018

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Slope
Polynomials
Integer
Bell Polynomials
Dyck Paths
Lattice Paths
Enumeration
Corollary
Partial
Language
Class

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

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title = "On factor-free Dyck words with half-integer slope",
abstract = "We study a class of rational Dyck paths with slope [Formula presented] 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.",
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year = "2018",
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On factor-free Dyck words with half-integer slope. / Birmajer, Daniel; Gil, Juan Bautista; Weiner, Michael David.

In: Advances in Applied Mathematics, Vol. 99, 01.08.2018, p. 94-108.

Research output: Contribution to journalArticle

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T1 - On factor-free Dyck words with half-integer slope

AU - Birmajer, Daniel

AU - Gil, Juan Bautista

AU - Weiner, Michael David

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N2 - We study a class of rational Dyck paths with slope [Formula presented] 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.

AB - We study a class of rational Dyck paths with slope [Formula presented] 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.

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