Geodesic
Exponential polynomial inequalities and monomial sum inequalities in $\rm p$-Newton sequences
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 793-819 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1007/s10587-016-0293-7
Classification : 11C20, 15A15, 15A18, 15A45
Keywords: exponential polynomial; Newton inequality; Newton coefficients; p-Newton sequence 
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Johnson, Charles R.; Marijuán, Carlos; Pisonero, Miriam; Yeh, Michael. Exponential polynomial inequalities and monomial sum inequalities in $\rm p$-Newton sequences. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 793-819. doi: 10.1007/s10587-016-0293-7

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