Guillermo Esteban, Clemens Huemer, Rodrigo I. Silveira
{"title":"New results on production matrices for geometric graphs","authors":"Guillermo Esteban, Clemens Huemer, Rodrigo I. Silveira","doi":"10.1016/j.endm.2018.06.037","DOIUrl":null,"url":null,"abstract":"<div><p>We present novel production matrices for non-crossing partitions, connected geometric graphs, and <em>k</em>-angulations, which provide another way of counting the number of such objects. For instance, a formula for the number of connected geometric graphs with given root degree, drawn on a set of <em>n</em> points in convex position in the plane, is presented. Further, we find the characteristic polynomials and we provide a characterization of the eigenvectors of the production matrices.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.037","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Notes in Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1571065318301288","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
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Abstract
We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another way of counting the number of such objects. For instance, a formula for the number of connected geometric graphs with given root degree, drawn on a set of n points in convex position in the plane, is presented. Further, we find the characteristic polynomials and we provide a characterization of the eigenvectors of the production matrices.
期刊介绍：
Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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