DOAJ Open Access 2007

Minimal and maximal plateau lengths in Motzkin paths

Helmut Prodinger Stephan Wagner

Lihat Sumber DOI

Abstrak

The minimal length of a plateau (a sequence of horizontal steps, preceded by an up- and followed by a down-step) in a Motzkin path is known to be of interest in the study of secondary structures which in turn appear in mathematical biology. We will treat this and the related parameters <i> maximal plateau length, horizontal segment </i>and <i>maximal horizontal segment </i>as well as some similar parameters in unary-binary trees by a pure generating functions approach―-Motzkin paths are derived from Dyck paths by a substitution process. Furthermore, we provide a pretty general analytic method to obtain means and limiting distributions for these parameters. It turns out that the maximal plateau and the maximal horizontal segment follow a Gumbel distribution.

Topik & Kata Kunci

Mathematics

Penulis (2)

Helmut Prodinger

Stephan Wagner

Format Sitasi

APA MLA BibTeX

Prodinger, H., Wagner, S. (2007). Minimal and maximal plateau lengths in Motzkin paths. https://doi.org/10.46298/dmtcs.3520

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.3520

Informasi Jurnal

Tahun Terbit: 2007
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.3520
Akses: Open Access ✓