On polynomials with interlacing zeros

1985 ◽  
pp. 255-258 ◽  
Author(s):  
M. Alvarez ◽  
G. Sansigre
Keyword(s):  
Interlacing Zeros

scholarly journals Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros

2013 ◽  
Vol 11 (5) ◽  
Author(s):  
James McKee ◽  
Chris Smyth
Keyword(s):  
Unit Circle ◽  
Special Class ◽  
Complete Classification ◽  
Cyclotomic Polynomials ◽  
Restricted Class ◽  
Integer Polynomials ◽  
Interlacing Zeros

AbstractWe give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also corresponds (in four different ways) to a single Pisot polynomial from a certain restricted class, the cyclogenic Pisot polynomials. We investigate properties of this class of Pisot polynomials.

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