| Title: | Combinatorial generation via permutation languages : Binary trees |
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| Authors: | ID Gregor, Petr (Author)
ID Mütze, Torsten (Author)
ID Namrata (Author) |
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| Files: |  1-s2.0-S0195669824001057-main.pdf (1,39 MB)
MD5: 0104332F3A7E489D7A5E78F8893F538F
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| Language: | English |
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| Work type: | Unknown |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FIŠ - Faculty of Information Studies in Novo mesto
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| Abstract: | In this paper we propose a notion of pattern avoidance in binary trees that generalizes the avoidance of contiguous tree patterns studied by Rowland and non-contiguous tree patterns studied by Dairyko, Pudwell, Tyner, and Wynn. Specifically, we propose algorithms for generating different classes of binary trees that are characterized by avoiding one or more of these generalized patterns. This is achieved by applying the recent Hartung–Hoang–Mütze– Williams generation framework, by encoding binary trees via permutations. In particular, we establish a one-to-one correspondence between tree patterns and certain mesh permutation patterns. We also conduct a systematic investigation of all tree patterns on at most 5 vertices, and we establish bijections between pattern-avoiding binary trees and other combinatorial objects, in particular pattern-avoiding lattice paths and set partitions. |
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| Keywords: | pattern avoidance, binary trees, mesh permutation patterns, combinatorial generation, algorithmic combinatorics |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 23.10.2023 |
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| Article acceptance date: | 12.06.2024 |
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| Publication date: | 18.07.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | str. 1-41 |
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| Numbering: | Vol. 122 |
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| PID: | 20.500.12556/ReVIS-11888  |
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| COBISS.SI-ID: | 241055235 |
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| UDC: | 519.17 |
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| ISSN on article: | 0195-6698 |
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| DOI: | 10.1016/j.ejc.2024.104020 |
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| Publication date in ReVIS: | 02.07.2025 |
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| Views: | 19 |
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| Downloads: | 0 |
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| Metadata: |    |
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