COEFFICIENTS AND ROOTS OF EHRHART POLYNOMIALS
COEFFICIENTS AND ROOTS OF EHRHART POLYNOMIALS
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EHRHART 多项式的系数和根
DOI：
10.1090/conm/374/06897
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Richard P. Stanley
中科院分区：
文献类型：
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作者：
M. Beck;J. D. Loera;M. Develin;Julian Pfeifle;Richard P. Stanley
凸格多面体的Ehrhart多项式对多面体的积分展开中的整数点进行计数。我们提出了由埃尔哈特多项式的系数所满足的新的线性不等式，并将它们与已知的不等式联系起来。我们也研究了Ehrhart多项式的根。我们证明了对于固定的d，在C上存在一个有界区域，其中包含了d-多边形的所有Ehrhart多项式的根，并且这些多项式的所有实根都在（- d，⌊d/2⌋）内。相反，我们证明了当维数d不固定时，正实数根可以任意大。最后对循环多面体和0/1多面体的Ehrhart多项式进行了实验研究。
The Ehrhart polynomial of a convex lattice polytope counts integer points in integral dilates of the polytope. We present new linear inequalities satisfied by the coeffi- cients of Ehrhart polynomials and relate them to known inequalities. We also investigate the roots of Ehrhart polynomials. We prove that for fixed d, there exists a bounded region of C containing all roots of Ehrhart polynomials of d-polytopes, and that all real roots of these polynomials lie in (−d, ⌊d/2⌋). In contrast, we prove that when the dimension d is not fixed the positive real roots can be arbitrarily large. We finish with an experimental investigation of the Ehrhart polynomials of cyclic polytopes and 0/1-polytopes.