On the linear independence of shifted powers

Autor: Ignacio García-Marco, Pascal Koiran, Timothée Pecatte

Publikováno v: Journal of Complexity
Journal of Complexity, 2018, 45, pp.67-82
Journal of Complexity, Elsevier, 2018, 45, pp.67-82

We call shifted power a polynomial of the form $(x-a)^e$. The main goal of this paper is to obtain broadly applicable criteria ensuring that the elements of a finite family $F$ of shifted powers are linearly independent or, failing that, to give a lo

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::332db7776aa2be681a8f2b8724c8b8d9
https://hal.science/hal-01520724v2/file/GarciaKoiranPecatte_submission_JCv2.pdf

Invertible polynomial mappings via Newton non-degeneracy

Autor: Mihai Tibăr, Luis Renato G. Dias, Ying Chen, Kiyoshi Takeuchi

Publikováno v: Annales de l'Institut Fourier
Annales de l'Institut Fourier, 2014, 64 (5), pp.1807-1822. ⟨10.5802/aif.2897⟩
Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2014, 64 (5), pp.1807-1822. ⟨10.5802/aif.2897⟩
Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2014, 64 (5), pp.1807-1822

We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.
Final ver

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e970ca539e14c5beaa155a4776057e56
http://arxiv.org/abs/1303.6879

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