Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Tropicalization and irreducibility of generalized Vandermonde determinants


Authors: Carlos D'Andrea and Luis Felipe Tabera
Journal: Proc. Amer. Math. Soc. 137 (2009), 3647-3656
MSC (2000): Primary 12E05; Secondary 14M12
Published electronically: June 12, 2009
MathSciNet review: 2529871
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We find geometric and arithmetic conditions in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix over the algebraic closure of any field $ k$. We also characterize those determinants whose tropicalization with respect to the variables of a row is irreducible.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 12E05, 14M12

Retrieve articles in all journals with MSC (2000): 12E05, 14M12


Additional Information

Carlos D'Andrea
Affiliation: Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via 585, E-08007 Barcelona, Spain
Email: cdandrea@ub.edu

Luis Felipe Tabera
Affiliation: Departamento de Matemáticas, Universidad de Cantabria, Estadística y Computación, Av. los Castros s/n, E-39005, Santander, Spain
Address at time of publication: Department of Mathematics, University of California, Berkeley, 893 Evans Hall #3840, Berkeley, California 94720-3840
Email: tabera@berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09951-1
PII: S 0002-9939(09)09951-1
Keywords: Vandermonde determinants, multivariate factorization, tropical geometry, valuations
Received by editor(s): March 14, 2008
Received by editor(s) in revised form: February 27, 2009
Published electronically: June 12, 2009
Additional Notes: The first author was supported by the Programa Ramón y Cajal and the Research Project grant MTM2007–67493 from the Ministerio de Educación y Ciencia, Spain.
The second author was supported by the Research Project grant MTM2005-08690-CO2-02 and a postdoctoral fellowship from the Ministerio de Educación y Ciencia, Spain
Communicated by: Martin Lorenz
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.