Small-Span Characteristic Polynomials of Integer Symmetric Matrices

被引:0
|
作者
McKee, James [1 ]
机构
[1] Univ London, Dept Math, Egham TW20 0EX, Surrey, England
来源
ALGORITHMIC NUMBER THEORY | 2010年 / 6197卷
关键词
ALGEBRAIC EQUATIONS; EIGENVALUES;
D O I
暂无
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
Let f(x) is an element of Z[x] be a totally real polynomial with roots alpha(1) <= ... <= alpha(d). The span of f(x) is defined to be alpha(d) - alpha(1). Monic irreducible f(x) of span less than 4 are special. In this paper we give a complete classification of those small-span polynomials which arise as characteristic polynomials of integer symmetric matrices. As one application, we find some low-degree polynomials that do not arise as the minimal polynomial of any integer symmetric matrix: these provide low-degree counterexamples to a conjecture of Estes and Guralnick [6].
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页码:270 / 284
页数:15
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