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https://hdl.handle.net/10216/119375
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DC Field | Value | Language |
---|---|---|
dc.creator | Duarte, R | |
dc.creator | António Guedes de Oliveira | |
dc.creator | Rui Duarte | |
dc.date.accessioned | 2022-09-10T18:26:55Z | - |
dc.date.available | 2022-09-10T18:26:55Z | - |
dc.date.issued | 2019 | |
dc.identifier.issn | 0196-8858 | |
dc.identifier.other | sigarra:321723 | |
dc.identifier.uri | https://hdl.handle.net/10216/119375 | - |
dc.description.abstract | Let 1 <= r <= n and suppose that, when the Depth-first Search Algorithm is applied to a given rooted labeled tree on n 1 vertices, exactly r vertices are visited before backtracking. Let R be the set of trees with this property. We count the number of elements of R. For this purpose, we first consider a bijection, due to Perkinson, Yang and Yu, that maps R onto the set of parking function with center (defined by the authors in a previous article) of size r. A second bijection maps this set onto the set of parking functions with run r, a property that we introduce here. We then prove that the number of length n parking functions with a given run is the number of length n rook words (defined by Leven, Rhoades and Wilson) with the same run. This is done by counting related lattice paths in a ladder shaped region. We finally count the number of length n rook words with run r, which is the answer to our initial question. | |
dc.language.iso | eng | |
dc.rights | restrictedAccess | |
dc.subject | Matemática, Matemática | |
dc.subject | Mathematics, Mathematics | |
dc.title | The number of parking functions with center of a given length | |
dc.type | Artigo em Revista Científica Internacional | |
dc.contributor.uporto | Faculdade de Ciências | |
dc.identifier.doi | 10.1016/j.aam.2019.02.004 | |
dc.identifier.authenticus | P-00Q-AVB | |
dc.subject.fos | Ciências exactas e naturais::Matemática | |
dc.subject.fos | Natural sciences::Mathematics | |
Appears in Collections: | FCUP - Artigo em Revista Científica Internacional |
Files in This Item:
File | Description | Size | Format | |
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321723.pdf Restricted Access | Artigo científico | 401.97 kB | Adobe PDF | Request a copy from the Author(s) |
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