scholarly journals Descartes' rule of signs, Newton polygons, and polynomials over hyperfields

2021 ◽  
Vol 569 ◽  
pp. 416-441
Author(s):  
Matthew Baker ◽  
Oliver Lorscheid
Keyword(s):  
Newton Polygons

scholarly journals Solution of tetrahedron equation and cluster algebras

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
P. Gavrylenko ◽  
M. Semenyakin ◽  
Y. Zenkevich
Keyword(s):  
Integrable System ◽  
Cluster Algebra ◽  
Newton Polygon ◽  
Cluster Algebras ◽  
Weyl Groups ◽  
Newton Polygons ◽  
Tetrahedron Equation ◽  
Affine Weyl Groups ◽  
New Formalism ◽  
Bruhat Cell

Abstract We notice a remarkable connection between the Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The tetrahedron transformation is then identified with a sequence of four mutations. As an application of the new formalism, we show how to construct an integrable system with the spectral curve with arbitrary symmetric Newton polygon. Finally, we embed this integrable system into the double Bruhat cell of a Poisson-Lie group, show how triangular decomposition can be used to extend our approach to the general non-symmetric Newton polygons, and prove the Lemma which classifies conjugacy classes in double affine Weyl groups of A-type by decorated Newton polygons.

scholarly journals Computing Galois groups by means of Newton polygons

2004 ◽  
Vol 115 (1) ◽  
pp. 71-84 ◽  
Author(s):  
Michael Kölle ◽  
Peter Schmid
Keyword(s):  
Galois Groups ◽  
Newton Polygons

Newton polygons

2012 ◽  
pp. 35-44
Author(s):  
Kiran S. Kedlaya
Keyword(s):  
Newton Polygons

scholarly journals A $$\tau $$ τ -Conjecture for Newton Polygons

2014 ◽  
Vol 15 (1) ◽  
pp. 185-197 ◽  
Author(s):  
Pascal Koiran ◽  
Natacha Portier ◽  
Sébastien Tavenas ◽  
Stéphan Thomassé
Keyword(s):  
Newton Polygons
Sign in / Sign up

Export Citation Format

Share Document