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Gale duality bounds on the location of roots of polynomials with nonnegative coefficients
dc.contributor.author | Pfeifle, Julián |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
dc.date.accessioned | 2010-06-21T13:37:21Z |
dc.date.available | 2010-06-21T13:37:21Z |
dc.date.created | 2010-04 |
dc.date.issued | 2010-04 |
dc.identifier.citation | Pfeifle, J. Gale duality bounds on the location of roots of polynomials with nonnegative coefficients. "Journal of combinatorial theory. Series A", Abril 2010, vol. 117, núm. 3, p. 248-271. |
dc.identifier.issn | 0097-3165 |
dc.identifier.uri | http://hdl.handle.net/2117/7768 |
dc.description.abstract | We bound the location of roots of polynomials that have nonnegative coefficients with respect to a fixed but arbitrary basis of the vector space of polynomials of degree at most d. For this, we interpret the basis polynomials as vector fields in the real plane, and at each point in the plane analyze the combinatorics of the Gale dual vector configuration. This approach permits us to incorporate arbitrary linear equations and inequalities among the coefficients in a unified manner to obtain more precise bounds on the location of roots. We apply our technique to bound the location of roots of Ehrhart and chromatic polynomials. Finally, we give an explanation for the clustering seen in plots of roots of random polynomials. |
dc.format.extent | 24 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::Matemàtica discreta::Combinatòria |
dc.subject.lcsh | Polynomials |
dc.subject.lcsh | Vector fields |
dc.subject.lcsh | Combinatorial analysis |
dc.title | Gale duality bounds on the location of roots of polynomials with nonnegative coefficients |
dc.type | Article |
dc.subject.lemac | Polinomis |
dc.subject.lemac | Camps vectorials |
dc.subject.lemac | Anàlisi combinatòria |
dc.contributor.group | Universitat Politècnica de Catalunya. MD - Matemàtica Discreta |
dc.identifier.doi | 10.1016/j.jcta.2009.10.009 |
dc.rights.access | Open Access |
local.identifier.drac | 2510429 |
dc.description.version | Postprint (published version) |
local.citation.author | Pfeifle, J. |
local.citation.publicationName | Journal of combinatorial theory. Series A |
local.citation.volume | 117 |
local.citation.number | 3 |
local.citation.startingPage | 248 |
local.citation.endingPage | 271 |
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