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Polynomials that Sign Represent Parity and Descartes’ Rule of Signs

✍ Scribed by Saugata Basu; Nayantara Bhatnagar; Parikshit Gopalan; Richard J. Lipton

Publisher: Springer
Year: 2008
Tongue: English
Weight: 566 KB
Volume: 17
Category: Article
ISSN: 1016-3328
DOI: 10.1007/s00037-008-0244-2

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📜 SIMILAR VOLUMES

On Descartes' rules of signs and their e

On Descartes' rules of signs and their exactness

✍ J. M. Peña 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 143 KB

## Abstract This paper revisits the Descartes' rules of signs and provides new bounds for the number of complex roots of a polynomial in certain complex regions. We also prove that the Descartes' rules associated with the Bernstein basis are exact for polynomials whose roots are real. (© 2005 WILEY

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Signs in the Laplace expansions and the parity of the distinguished representatives

✍ Lin Tan 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 616 KB

In this paper, the signs of the terms in the Laplace expansions of determinants are investigated. The problem is equivalent to that of the parity of the distinguished coset representatives for the (maximal) parabolic subgroups of the symmetric groups. The number of positive and negative terms (equiv