Pólya’s Theorem with zeros
 Citation data:

Journal of Symbolic Computation, ISSN: 07477171, Vol: 46, Issue: 9, Page: 10391048
 Publication Year:
 2011
 Repository URL:
 https://digitalcommons.kennesaw.edu/facpubs/1464
 DOI:
 10.1016/j.jsc.2011.05.006
 Author(s):
 Publisher(s):
 Tags:
 Mathematics; POLYNOMIAL rings; COMBINATORIAL analysis; VARIABLES; NONnegative matrices; MATHEMATICAL analysis; MATHEMATICAL constants; Analysis; Applied Mathematics
article description
Let R[X] be the real polynomial ring in n variables. Pólya’s Theorem says that if a homogeneous polynomial p∈R[X] is positive on the standard n simplex Δn, then for sufficiently large N all the coefficients of (X1+⋯+Xn)Np are positive. We give a complete characterization of forms, possibly with zeros on Δn, for which there exists N so that all coefficients of (X1+⋯+Xn)Np have only nonnegative coefficients, along with a bound on the N needed.