The height of random binary unlabelled trees
This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a central and local sense. Moderate as well as large deviations e...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2008-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3559/pdf |
| _version_ | 1797270417814061056 |
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| author | Nicolas Broutin Philippe Flajolet |
| author_facet | Nicolas Broutin Philippe Flajolet |
| author_sort | Nicolas Broutin |
| collection | DOAJ |
| description | This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a central and local sense. Moderate as well as large deviations estimates are also derived. The proofs rely on the analysis (in the complex plane) of generating functions associated with trees of bounded height. |
| first_indexed | 2024-04-25T02:03:57Z |
| format | Article |
| id | doaj.art-5fe341b86eb24d3cafb7fa5dfb86dd39 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:57Z |
| publishDate | 2008-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-5fe341b86eb24d3cafb7fa5dfb86dd392024-03-07T14:36:56ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502008-01-01DMTCS Proceedings vol. AI,...Proceedings10.46298/dmtcs.35593559The height of random binary unlabelled treesNicolas Broutin0Philippe Flajolet1AlgorithmsAlgorithmsThis extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a central and local sense. Moderate as well as large deviations estimates are also derived. The proofs rely on the analysis (in the complex plane) of generating functions associated with trees of bounded height.https://dmtcs.episciences.org/3559/pdfaverage case analysisheightlimit distributionlocal limit theoremgenerating functions[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-ds] mathematics [math]/dynamical systems [math.ds][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Nicolas Broutin Philippe Flajolet The height of random binary unlabelled trees Discrete Mathematics & Theoretical Computer Science average case analysis height limit distribution local limit theorem generating functions [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-ds] mathematics [math]/dynamical systems [math.ds] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | The height of random binary unlabelled trees |
| title_full | The height of random binary unlabelled trees |
| title_fullStr | The height of random binary unlabelled trees |
| title_full_unstemmed | The height of random binary unlabelled trees |
| title_short | The height of random binary unlabelled trees |
| title_sort | height of random binary unlabelled trees |
| topic | average case analysis height limit distribution local limit theorem generating functions [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-ds] mathematics [math]/dynamical systems [math.ds] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/3559/pdf |
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