Characterization of polynomials whose large powers have all positive coefficients
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- by Colin Tan and Wing-Keung To PDF
- Proc. Amer. Math. Soc. 146 (2018), 589-600 Request permission
Abstract:
We give a criterion which characterizes a homogeneous real multi-variate polynomial to have the property that all sufficiently large powers of the polynomial (as well as their products with any given positive homogeneous polynomial) have all positive coefficients. Our result generalizes a result of De Angelis, which corresponds to the case of homogeneous bivariate polynomials, as well as a classical result of Pólya, which corresponds to the case of a specific linear polynomial. As an application, we also give a characterization of certain polynomial spectral radius functions of the defining matrix functions of Markov chains.References
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Additional Information
- Colin Tan
- Affiliation: Department of Statistics & Applied Probability, National University of Singapore, Block S16, 6 Science Drive 2, Singapore 117546
- Address at time of publication: General Education Unit, Office of the Provost, National University of Singapore, 21 Lower Kent Ridge Road, Singapore 119077
- MR Author ID: 1141365
- Email: colinwytan@gmail.com
- Wing-Keung To
- Affiliation: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076
- MR Author ID: 267228
- Email: mattowk@nus.edu.sg
- Received by editor(s): January 8, 2017
- Received by editor(s) in revised form: February 20, 2017
- Published electronically: October 23, 2017
- Additional Notes: The second author was partially supported by the research grant R-146-000-142-112 from the National University of Singapore and the Ministry of Education
- Communicated by: Franc Forstnerič
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 589-600
- MSC (2010): Primary 26C05, 12D99, 32T15
- DOI: https://doi.org/10.1090/proc/13709
- MathSciNet review: 3731694