Minimal and maximal plateau lengths in Motzkin paths
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> max...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2007-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3520/pdf |
| _version_ | 1827324064786546688 |
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| author | Helmut Prodinger Stephan Wagner |
| author_facet | Helmut Prodinger Stephan Wagner |
| author_sort | Helmut Prodinger |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:03:52Z |
| format | Article |
| id | doaj.art-4d9a43525fac44b3b8ef6515aeb5e917 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:52Z |
| publishDate | 2007-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-4d9a43525fac44b3b8ef6515aeb5e9172024-03-07T14:34:52ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502007-01-01DMTCS Proceedings vol. AH,...Proceedings10.46298/dmtcs.35203520Minimal and maximal plateau lengths in Motzkin pathsHelmut Prodinger0Stephan Wagner1Department of Mathematical Sciences [Matieland, Stellenbosch Uni.]Department of Mathematical Sciences [Matieland, Stellenbosch Uni.]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.https://dmtcs.episciences.org/3520/pdfgumbel distributionunary-binary treesmotzkin pathssingularity analysismellin transformbootstrapping[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds][info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co][info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| spellingShingle | Helmut Prodinger Stephan Wagner Minimal and maximal plateau lengths in Motzkin paths Discrete Mathematics & Theoretical Computer Science gumbel distribution unary-binary trees motzkin paths singularity analysis mellin transform bootstrapping [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| title | Minimal and maximal plateau lengths in Motzkin paths |
| title_full | Minimal and maximal plateau lengths in Motzkin paths |
| title_fullStr | Minimal and maximal plateau lengths in Motzkin paths |
| title_full_unstemmed | Minimal and maximal plateau lengths in Motzkin paths |
| title_short | Minimal and maximal plateau lengths in Motzkin paths |
| title_sort | minimal and maximal plateau lengths in motzkin paths |
| topic | gumbel distribution unary-binary trees motzkin paths singularity analysis mellin transform bootstrapping [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| url | https://dmtcs.episciences.org/3520/pdf |
| work_keys_str_mv | AT helmutprodinger minimalandmaximalplateaulengthsinmotzkinpaths AT stephanwagner minimalandmaximalplateaulengthsinmotzkinpaths |