Exponential polynomial inequalities and monomial sum inequalities in $p$-Newton sequences

Czechoslovak Mathematical Journal

Carlos Marijuán¹  Johnson²  Charles R. ³  Miriam Pisonero⁴ 

[1] (corresponding author), Departamento Matemática Aplicada, E.T.S. de Arquitectura, Avenida de Salamanca 18, 47014-Valladolid, Spain;Departamento Matemática Aplicada, Escuela de Ingeniería Informática, Paseo de Belén 15, 47011-Valladolid, Spain, email:;Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia, 23187-8795, USA;Purdue University, 610 Purdue Mall, West Lafayette, Indiana, 47907 USA

关键词: exponential polynomial;    Newton inequality;    Newton coefficients;    p-Newton sequence;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

We consider inequalities between sums of monomials that hold for all p-Newton sequences. This continues recent work in which inequalities between sums of two, two-term monomials were combinatorially characterized (via the indices involved). Our focus is on the case of sums of three, two-term monomials, but this is very much more complicated. We develop and use a theory of exponential polynomial inequalities to give a sufficient condition for general monomial sum inequalities, and use the sufficient condition in two ways. The sufficient condition is necessary in the case of sums of two monomials but is not known if it is for sums of more. A complete description of the desired inequalities is given for Newton sequences of less than 5 terms.

【 授权许可】

Unknown