C. Hillar

activity

20022008

most citedFibonacci Identities and Graph Colorings

8 citations · 12 across the 12 of their papers we have counts for

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Showing 2007Show all

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math-ph2007★ 2 cited

On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices

Christopher J. Hillar, Charles R. Johnson

It is shown that the polynomial \[p(t) = \text{Tr}[(A+tB)^m]\] has positive coefficients when $m = 6$ and $A$ and $B$ are any two 3-by-3 complex Hermitian positive definite matrice…

math.AC2007

Sums of squares over totally real fields are rational sums of squares

Christopher J. Hillar

Let $K$ be a totally real number field with Galois closure $L$ . We prove that if $f \in Q [x_{1}, ..., x_{n}]$ is a sum of $m$ squares in $K [x_{1}, ..., x_{n}]$ , then $f$ is a sum of \[…