PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 66(80), pp. 16--22 (1999)
Universal counting of lattice points in polytopes
Imre Bárány and Jean-Michel KantorMathematical Institute of the Hungarian Academy of Sciences POB 127, 1364 Budapest, Hungary and Université Paris 7, 4 Place Jussieu, Institut Mathématique de Jussieu, 75252 Paris, France
Abstract: Given a lattice polytope $P$ (with underlying lattice $\lo$), the universal counting function $\uu_P(\lo')=|P\cap \lo'|$ is defined on all lattices $\lo'$ containing $\lo$. Motivated by questions concerning lattice polytopes and the Ehrhart polynomial, we study the equation $\uu_P=\uu_Q$.
Classification (MSC2000): 52B20; 52A27
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts