Combinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks

Abstract The combinatorial study of phylogenetic networks has attracted much attention in recent times. In particular, one class of them, the so-called tree-child networks, are becoming the most prominent ones. However, their combinatorial properties are largely unknown. In this paper we address the...

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Autores principales:	Miquel Pons, Josep Batle
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/367bafac32804daeac8c8a08b43b1e69
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spelling	oai:doaj.org-article:367bafac32804daeac8c8a08b43b1e692021-11-14T12:22:42ZCombinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks10.1038/s41598-021-01166-w2045-2322https://doaj.org/article/367bafac32804daeac8c8a08b43b1e692021-11-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-01166-whttps://doaj.org/toc/2045-2322Abstract The combinatorial study of phylogenetic networks has attracted much attention in recent times. In particular, one class of them, the so-called tree-child networks, are becoming the most prominent ones. However, their combinatorial properties are largely unknown. In this paper we address the problem of exactly counting them. We conjecture a relationship with the cardinality of a certain class of words. By solving the counting problem for the words, and on the basis of the conjecture, several simple recurrence formulas for general cases arise. Moreover, a precise asymptotic analysis is provided. Our results coincide with all current formulas in the literature for particular subclasses of tree-child networks, as well as with numerical results obtained for small networks. We expect that the study of the relationship between the newly defined words and the networks will lead to further combinatoric characterizations of this class of phylogenetic networks.Miquel PonsJosep BatleNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-14 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Miquel Pons Josep Batle Combinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks
description	Abstract The combinatorial study of phylogenetic networks has attracted much attention in recent times. In particular, one class of them, the so-called tree-child networks, are becoming the most prominent ones. However, their combinatorial properties are largely unknown. In this paper we address the problem of exactly counting them. We conjecture a relationship with the cardinality of a certain class of words. By solving the counting problem for the words, and on the basis of the conjecture, several simple recurrence formulas for general cases arise. Moreover, a precise asymptotic analysis is provided. Our results coincide with all current formulas in the literature for particular subclasses of tree-child networks, as well as with numerical results obtained for small networks. We expect that the study of the relationship between the newly defined words and the networks will lead to further combinatoric characterizations of this class of phylogenetic networks.
format	article
author	Miquel Pons Josep Batle
author_facet	Miquel Pons Josep Batle
author_sort	Miquel Pons
title	Combinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks
title_short	Combinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks
title_full	Combinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks
title_fullStr	Combinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks
title_full_unstemmed	Combinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks
title_sort	combinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/367bafac32804daeac8c8a08b43b1e69
work_keys_str_mv	AT miquelpons combinatorialcharacterizationofacertainclassofwordsandaconjecturedconnectionwithgeneralsubclassesofphylogenetictreechildnetworks AT josepbatle combinatorialcharacterizationofacertainclassofwordsandaconjecturedconnectionwithgeneralsubclassesofphylogenetictreechildnetworks
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Combinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks

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