Deepest Nodes in Marked Ordered Trees
A variation of ordered trees, where each rightmost edge might be marked or not, if it does not lead to an endnode, is investigated. These marked ordered trees were introduced by E. Deutsch et al. to model skew Dyck paths. We study the number of deepest nodes in such trees. Explicit generating functi...
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| Format: | Article |
| Language: | English |
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Sciendo
2022-09-01
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| Series: | Annales Mathematicae Silesianae |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amsil-2022-0015 |
| _version_ | 1797989217216757760 |
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| author | Prodinger Helmut |
| author_facet | Prodinger Helmut |
| author_sort | Prodinger Helmut |
| collection | DOAJ |
| description | A variation of ordered trees, where each rightmost edge might be marked or not, if it does not lead to an endnode, is investigated. These marked ordered trees were introduced by E. Deutsch et al. to model skew Dyck paths. We study the number of deepest nodes in such trees. Explicit generating functions are established and the average number of deepest nodes, which approaches 53{5 \over 3} when the number of nodes gets large. This is to be compared to standard ordered trees where the average number of deepest nodes approaches 2. |
| first_indexed | 2024-04-11T08:15:38Z |
| format | Article |
| id | doaj.art-1b483eaff8b24c89b3e3b994a6bc889f |
| institution | Directory Open Access Journal |
| issn | 2391-4238 |
| language | English |
| last_indexed | 2024-04-11T08:15:38Z |
| publishDate | 2022-09-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Mathematicae Silesianae |
| spelling | doaj.art-1b483eaff8b24c89b3e3b994a6bc889f2022-12-22T04:35:09ZengSciendoAnnales Mathematicae Silesianae2391-42382022-09-0136221522710.2478/amsil-2022-0015Deepest Nodes in Marked Ordered TreesProdinger Helmut0Department of Mathematical Sciences, Stellenbosch University, 7602StellenboschSouth Africaand NITheCS (National Institute for Theoretical and Computational Sciences)South AfricaA variation of ordered trees, where each rightmost edge might be marked or not, if it does not lead to an endnode, is investigated. These marked ordered trees were introduced by E. Deutsch et al. to model skew Dyck paths. We study the number of deepest nodes in such trees. Explicit generating functions are established and the average number of deepest nodes, which approaches 53{5 \over 3} when the number of nodes gets large. This is to be compared to standard ordered trees where the average number of deepest nodes approaches 2.https://doi.org/10.2478/amsil-2022-0015marked ordered treesskew dyck pathsgenerating functions05a15 |
| spellingShingle | Prodinger Helmut Deepest Nodes in Marked Ordered Trees Annales Mathematicae Silesianae marked ordered trees skew dyck paths generating functions 05a15 |
| title | Deepest Nodes in Marked Ordered Trees |
| title_full | Deepest Nodes in Marked Ordered Trees |
| title_fullStr | Deepest Nodes in Marked Ordered Trees |
| title_full_unstemmed | Deepest Nodes in Marked Ordered Trees |
| title_short | Deepest Nodes in Marked Ordered Trees |
| title_sort | deepest nodes in marked ordered trees |
| topic | marked ordered trees skew dyck paths generating functions 05a15 |
| url | https://doi.org/10.2478/amsil-2022-0015 |
| work_keys_str_mv | AT prodingerhelmut deepestnodesinmarkedorderedtrees |