On Path diagrams and Stirling permutations
- A permutation can be locally classified according to the four local types: peaks, valleys, double rises and double falls. The corresponding classification of binary increasing trees uses four different types of nodes. Flajolet demonstrated the continued fraction representation of the generating function of local types, using a classical bijection between permutations, binary increasing trees, and suitably defined path diagrams induced by Motzkin paths.
The aim of this article is to extend the notion of local types from permutations to k-Stirling permutations (also known as k-multipermutations). We establish a bijection of these local types to node types of (k+1)-ary increasing trees. We present a branched continued fraction representation of the generating function of these local types through a bijection with path diagrams induced by Łukasiewicz paths, generalizing the results from permutations to arbitrary k-Stirling permutations.
We further show that the generating function of ordinary Stirling permutation has at least three branched continued fraction representations, using correspondences between non-standard increasing trees, k-Stirling permutations and path diagrams.
MetadatenAuthor: | Markus Kuba, Anna Varvak |
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Parent Title (English): | Séminaire Lotharingien de Combinatoire |
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Document Type: | Article |
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Language: | English |
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Completed Date: | 2021/06/15 |
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Date of first Publication: | 2021/12/15 |
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Responsibility for metadata: | Fachhochschule Technikum Wien |
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Release Date: | 2021/12/15 |
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GND Keyword: | Continued fractions; Formale Potenzreihe; Increasing trees; Kettenbruch; Multipermutations; Path diagrams; Stirling permutations; Łukasiewicz paths |
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Issue: | B82c (2021) |
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Pagenumber: | 28 |
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Publish on Website: | 1 |
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Open Access: | 1 |
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Reviewed: | 0 |
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Link to Publication: | https://www.mat.univie.ac.at/~slc/wpapers/s82kuba.html |
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Department: | Department Angewandte Mathematik und Physik |
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Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik |
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Research Focus: | Sonstiges |
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Projects: | Import |
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Studienjahr: | 2020/2021 |
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