34 citations · 52 across the 9 of their papers we have counts for
10 papers
Short Salem polynomials
James McKee, Chris Smyth
We give a complete classification of all Salem polynomials of length 5. For length 6 we show that all but finitely many Salem polynomials lie in one of 12 infinite families, and su…
The Cassels heights of cyclotomic integers
James McKee, Byeong-Kweon Oh, Chris Smyth
We study the set of mean square values of the moduli of the conjugates of cyclotomic integers . For its th derived set , we show that $\mathscr…
Symmetrizable integer matrices having all their eigenvalues in the interval [-2,2]
James McKee, Chris Smyth
The adjacency matrices of graphs form a special subset of the set of all integer symmetric matrices. The description of which graphs have all their eigenvalues in the interval [-2,…
A classification of all 1-Salem graphs
Lee Gumbrell, James McKee
One way to study certain classes of polynomials is by considering examples that are attached to combinatorial objects. Any graph has an associated reciprocal polynomial ,…
Salem numbers and Pisot numbers via interlacing
James McKee, Chris Smyth
We present a general construction of Salem numbers via rational functions whose zeros and poles mostly lie on the unit circle and satisfy an interlacing condition. This extends and…
Constructing k-radius sequences
Simon R. Blackburn, James F. McKee
An n-ary k-radius sequence is a finite sequence of elements taken from an alphabet of size n such that any two distinct elements of the alphabet occur within distance k of each oth…