C. Hillar

activity

20022005

most citedPolynomial recurrences and cyclic resultants

2 citations · 2 across the 8 of their papers we have counts for

collaborators

8 papers

math.MG2005

A Result About the Density of Iterated Line Intersections in the Plane

Christopher J. Hillar, Darren L. Rhea

Let $S$ be a finite set of points in the plane and let $T (S)$ be the set of intersection points between pairs of lines passing through any two points in $S$ . We character…

math.OA2005

Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

Christopher Hillar, Charles R. Johnson

We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$ . The question of which words have only positive…

math.OA2005

Positive eigenvalues and two-letter generalized words

Christopher Hillar, Charles R. Johnson, Ilya M. Spitkovsky

A generalized word in two letters $A$ and $B$ is an expression of the form $W = A^{α_{1}} B^{β_{1}} A^{α_{2}} B^{β_{2}} ... A^{α_{N}} B^{β_{N}}$ in which the exponents $α_{i}$ , $β_{i}$ are nonzero real n…

math.OA2005

Absolutely Flat Idempotents

Jonathan M. Groves, Yonatan Harel, Christopher J. Hillar +2

A real $n$ -by- $n$ idempotent matrix $A$ with all entries having the same absolute value is called {\it absolutely flat}. We consider the possible ranks of such matrices and herein…

math.AG2004★ 2 cited

Polynomial recurrences and cyclic resultants

Christopher J. Hillar, Lionel Levine

Let $K$ be an algebraically closed field of characteristic zero and let $f \in K [x]$ . The $m$ -th {\it cyclic resultant} of $f$ is \[r_m = \text{Res}(f,x^m-1).\] A generic monic pol…

math.AC2004

Cyclic Resultants

Christopher J. Hillar

We characterize polynomials having the same set of nonzero cyclic resultants. Generically, for a polynomial $f$ of degree $d$ , there are exactly $2^{d - 1}$ distinct degree $d$ polyn…