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dc.contributor.authorÁvila Ramírez, Nicolásspa
dc.contributor.otherCarrillo Torres, Sergio A.spa
dc.contributor.otherGonzález D’León, Rafael S.spa
dc.date.accessioned2022-07-05T20:10:06Zspa
dc.date.available2022-07-05T20:10:06Zspa
dc.date.created2022spa
dc.date.issued2022spa
dc.identifier.citationÁvila Ramírez, N. (2022). The µ-polynomials of graph associahedra. [Tesis de maestría]. Universidad Sergio Arboleda.eng
dc.identifier.urihttp://hdl.handle.net/11232/1821eng
dc.description.abstractWe study two polynomials associated to a graph G that are of interest in the recent literature. The first one is the h-polynomial of the graph-associahedron of G defined by Carr and Devadoss. The second one is the μ-polynomial recently defined by González D’León and Wachs, which in the case of trees the authors conjecture that is up to sign equal to its h-polynomial. We prove a more general relation between the h- and the μ-polynomial of G which in the special case of trees proves González D’León - Wachs’ conjecture. We give a new description of the μ-polynomials in terms of a family of forests that we call μ-forests. As applications of the tools developed, we compute the μ- polynomials of the families of cycle and kite-like graphs. These are related to the Narayana polynomials of type A and B. We also show that these families of polynomials are realrooted and form interlacing sequences giving support and extending previous conjectures to a general conjecture on real-rootedness and the interlacing property of the h- and the μ-polynomials of an arbitrary graph G.eng
dc.format.extent93spa
dc.format.mimetypeapplication/pdfeng
dc.publisherUniversidad Sergio Arboledaspa
dc.rightshttps://repository.usergioarboleda.edu.co/bitstream/id/bf9935e7-89e0-4f90-857e-155cba0b7f4c/license.txtspa
dc.titleThe μ-polynomials of graph associahedra.spa
dc.subject.lembPolinomiosspa
dc.subject.lembArboles (Teoría de grafosspa
dc.subject.lembTeoría de grafosspa
dc.publisher.programMaestría en Matemáticas Aplicadasspa
dc.type.coarversionhttp://purl.org/coar/version/c_970fb48d4fbd8a85eng
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aaeng
dc.publisher.departmentEscuela de Postgradosspa
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dc.type.coarhttp://purl.org/coar/resource_type/c_bdcceng
dc.type.localTesis/Trabajo de grado - Monografía - Maestríaspa
dc.description.degreenameMagister en Matemáticas Aplicadasspa
dc.description.degreelevelMaestríaspa


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