Enumeration of rooted 3-connected bipartite planar maps

We provide the first solution to the problem of counting rooted 3-connected bipartite planar maps. Our starting point is the enumeration of bicoloured planar maps according to the number of edges and monochromatic edges, following Bernardi and Bousquet-Mélou [J. Comb. Theory Ser. B, 101 (2011), 315–...

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Autores: Noy Serrano, Marcos|||0000-0002-2399-1359, Requile, Clement|||0000-0002-7689-7972, Rué Perna, Juan José|||0000-0002-6420-3179
Formato: artículo
Fecha de publicación:2024
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/406360
Acesso em linha:https://hdl.handle.net/2117/406360
https://dx.doi.org/10.5802/crmath.548
Access Level:acceso abierto
Palavra-chave:Combinatorial analysis
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
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spelling Enumeration of rooted 3-connected bipartite planar mapsÉnumération des cartes planaires enracinées biparties et 3-connexesNoy Serrano, Marcos|||0000-0002-2399-1359Requile, Clement|||0000-0002-7689-7972Rué Perna, Juan José|||0000-0002-6420-3179Combinatorial analysisCombinacions (Matemàtica)Classificació AMS::05 CombinatoricsÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::CombinatòriaWe provide the first solution to the problem of counting rooted 3-connected bipartite planar maps. Our starting point is the enumeration of bicoloured planar maps according to the number of edges and monochromatic edges, following Bernardi and Bousquet-Mélou [J. Comb. Theory Ser. B, 101 (2011), 315–377]. The decomposition of a map into 2- and 3-connected components allows us to obtain the generating functions of 2- and 3-connected bicoloured maps. Setting to zero the variable marking monochromatic edges we obtain the generating function of 3-connected bipartite maps, which is algebraic of degree 26. We deduce from it an asymptotic estimate for the number of 3-connected bipartite planar maps of the form t n-5/2¿ n, where ¿ = ¿ -1 ˜ 2.40958 and ¿ ˜ 0.41501 is an algebraic number of degree 10.The authors acknowledge the financial support of the Spanish State Research Agency through projects MTM2017-82166-P, PID2020-113082GB-I00, and the Marie Curie RISE research network ’RandNet’ MSCA-RISE-2020-101007705. Additionally, M.N. and J.R. acknowledge support from the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence (CEX2020-001084-M), and C.R. acknowledges support from the grant Beatriu de Pinós BP2019, funded by the H2020 COFUND project No 801370 and AGAUR (the Catalan agency for management of university and research grants).Peer Reviewed20242024-03-0720242024-04-11journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/406360https://dx.doi.org/10.5802/crmath.548reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-82166-P COMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICAAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113082GB-I00 COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4063602026-05-27T15:37:01Z
dc.title.none.fl_str_mv Enumeration of rooted 3-connected bipartite planar maps
Énumération des cartes planaires enracinées biparties et 3-connexes
title Enumeration of rooted 3-connected bipartite planar maps
spellingShingle Enumeration of rooted 3-connected bipartite planar maps
Noy Serrano, Marcos|||0000-0002-2399-1359
Combinatorial analysis
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
title_short Enumeration of rooted 3-connected bipartite planar maps
title_full Enumeration of rooted 3-connected bipartite planar maps
title_fullStr Enumeration of rooted 3-connected bipartite planar maps
title_full_unstemmed Enumeration of rooted 3-connected bipartite planar maps
title_sort Enumeration of rooted 3-connected bipartite planar maps
dc.creator.none.fl_str_mv Noy Serrano, Marcos|||0000-0002-2399-1359
Requile, Clement|||0000-0002-7689-7972
Rué Perna, Juan José|||0000-0002-6420-3179
author Noy Serrano, Marcos|||0000-0002-2399-1359
author_facet Noy Serrano, Marcos|||0000-0002-2399-1359
Requile, Clement|||0000-0002-7689-7972
Rué Perna, Juan José|||0000-0002-6420-3179
author_role author
author2 Requile, Clement|||0000-0002-7689-7972
Rué Perna, Juan José|||0000-0002-6420-3179
author2_role author
author
dc.subject.none.fl_str_mv Combinatorial analysis
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
topic Combinatorial analysis
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
description We provide the first solution to the problem of counting rooted 3-connected bipartite planar maps. Our starting point is the enumeration of bicoloured planar maps according to the number of edges and monochromatic edges, following Bernardi and Bousquet-Mélou [J. Comb. Theory Ser. B, 101 (2011), 315–377]. The decomposition of a map into 2- and 3-connected components allows us to obtain the generating functions of 2- and 3-connected bicoloured maps. Setting to zero the variable marking monochromatic edges we obtain the generating function of 3-connected bipartite maps, which is algebraic of degree 26. We deduce from it an asymptotic estimate for the number of 3-connected bipartite planar maps of the form t n-5/2¿ n, where ¿ = ¿ -1 ˜ 2.40958 and ¿ ˜ 0.41501 is an algebraic number of degree 10.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-03-07
2024
2024-04-11
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/406360
https://dx.doi.org/10.5802/crmath.548
url https://hdl.handle.net/2117/406360
https://dx.doi.org/10.5802/crmath.548
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-82166-P COMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICA
Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113082GB-I00 COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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