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Characteristic polynomials of production matrices for geometric graphs
dc.contributor.author | Huemer, Clemens |
dc.contributor.author | Pilz, Alexander |
dc.contributor.author | Seara Ojea, Carlos |
dc.contributor.author | Silveira, Rodrigo Ignacio |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2017-12-11T09:53:39Z |
dc.date.available | 2019-02-01T01:31:06Z |
dc.date.issued | 2017-08-01 |
dc.identifier.citation | Huemer, C., Pilz, A., Seara, C., Silveira, R.I. Characteristic polynomials of production matrices for geometric graphs. "Electronic notes in discrete mathematics", 1 Agost 2017, vol. 61, p. 1-7. |
dc.identifier.issn | 1571-0653 |
dc.identifier.uri | http://hdl.handle.net/2117/111649 |
dc.description.abstract | An n×n production matrix for a class of geometric graphs has the property that the numbers of these geometric graphs on up to n vertices can be read off from the powers of the matrix. Recently, we obtained such production matrices for non-crossing geometric graphs on point sets in convex position [Huemer, C., A. Pilz, C. Seara, and R.I. Silveira, Production matrices for geometric graphs, Electronic Notes in Discrete Mathematics 54 (2016) 301–306]. In this note, we determine the characteristic polynomials of these matrices. Then, the Cayley-Hamilton theorem implies relations among the numbers of geometric graphs with different numbers of vertices. Further, relations between characteristic polynomials of production matrices for geometric graphs and Fibonacci numbers are revealed. |
dc.description.sponsorship | This project has received funding from the European Union’s Horizon 89 2020 research and innovation programme under the Marie Sk lodowska- 90 Curie grant agreement No 734922. 91 C. H., C. S., and R. I. S. were partially supported by projects MINECO MTM2015- 92 63791-R and Gen. Cat. DGR2014SGR46. R. I. S. was also supported by MINECO 93 through the Ramon y Cajal program |
dc.format.extent | 7 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria |
dc.subject.lcsh | Graph theory |
dc.subject.other | Fibonacci number |
dc.subject.other | geometric graph |
dc.subject.other | production matrix |
dc.subject.other | Riordan array |
dc.title | Characteristic polynomials of production matrices for geometric graphs |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
dc.identifier.doi | 10.1016/j.endm.2017.07.017 |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S1571065317301828?via%3Dihub |
dc.rights.access | Open Access |
local.identifier.drac | 21554360 |
dc.description.version | Postprint (published version) |
local.citation.author | Huemer, C.; Pilz, A.; Seara, C.; Silveira, R.I. |
local.citation.publicationName | Electronic notes in discrete mathematics |
local.citation.volume | 61 |
local.citation.startingPage | 1 |
local.citation.endingPage | 7 |
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