Deciding eventual positivity of polynomials

Deciding positivity of real polynomials

We describe an algorithm for deciding whether or not a real polynomial is positive semideenite. The question is reduced to deciding whether or not a certain zero-dimensional system of polynomial equations has a real root.

Ela Sign Patterns That Allow Eventual Positivity

Several necessary or sufficient conditions for a sign pattern to allow eventual positivity are established. It is also shown that certain families of sign patterns do not allow eventual positivity. These results are applied to show that for n ≥ 2, the minimum number of positive entries in an n×n sign pattern that allows eventual positivity is n+1, and to classify all 2×2 and 3×3 sign patterns a...

Sign patterns that allow eventual positivity

Several necessary or sufficient conditions for a sign pattern to allow eventual positivity are established. It is also shown that certain families of sign patterns do not allow eventual positivity. These results are applied to show that for n ≥ 2, the minimum number of positive entries in an n×n sign pattern that allows eventual positivity is n+1, and to classify all 2×2 and 3×3 sign patterns a...

Positivity Of Trigonometri Polynomials

Deciding Positivity of Littlewood-Richardson Coefficients

Starting with Knutson and Tao’s hive model [KT99], we characterize the Littlewood– Richardson coefficient c λ,μ of given partitions λ, μ, ν ∈ N as the number of capacity achieving hive flows on the honeycomb graph. Based on this, we design a polynomial time algorithm for deciding c λ,μ > 0. This algorithm is easy to state and takes O (