TY - JOUR

T1 - The minimum period of the Ehrhart quasi-polynomial of a rational polytope

AU - McAllister, T.B.

AU - Woods, K.M.

PY - 2005

Y1 - 2005

N2 - If is a rational polytope, then is a quasi-polynomial in n, called the Ehrhart quasi-polynomial of P. The minimum period of iP(n) must divide . Few examples are known where the minimum period is not exactly . We show that for any , there is a 2-dimensional triangle P such that but such that the minimum period of iP(n) is 1, that is, iP(n) is a polynomial in n. We also characterize all polygons P such that iP(n) is a polynomial. In addition, we provide a counterexample to a conjecture by T. Zaslavsky about the periods of the coefficients of the Ehrhart quasi-polynomial.

AB - If is a rational polytope, then is a quasi-polynomial in n, called the Ehrhart quasi-polynomial of P. The minimum period of iP(n) must divide . Few examples are known where the minimum period is not exactly . We show that for any , there is a 2-dimensional triangle P such that but such that the minimum period of iP(n) is 1, that is, iP(n) is a polynomial in n. We also characterize all polygons P such that iP(n) is a polynomial. In addition, we provide a counterexample to a conjecture by T. Zaslavsky about the periods of the coefficients of the Ehrhart quasi-polynomial.

U2 - 10.1016/j.jcta.2004.08.006

DO - 10.1016/j.jcta.2004.08.006

M3 - Article

SN - 0097-3165

VL - 109

SP - 345

EP - 352

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

IS - 2

ER -