Inside-out polytopes
Inside-out polytopes
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DOI：
10.1016/j.aim.2005.07.006
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发表时间：
2003-09
影响因子：
1.7
通讯作者：
M. Beck;T. Zaslavsky
中科院分区：
文献类型：
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作者：
M. Beck;T. Zaslavsky
给出了有理多面体中点阵点计数的一般推广和适当图着色的列举，图上无零流，幻方与图，反幻方与图，部分不同整数的组成，以及广义拉丁方。我们的方法是将Ehrhart的格点计数理论推广到一个由超平面排列解剖的凸多面体。我们特别开发了图形和符号图着色、整数组成和反魔术标记的应用。
We present a common generalization of counting lattice points in rational polytopes and the enumeration of proper graph colorings, nowhere-zero flows on graphs, magic squares and graphs, antimagic squares and graphs, compositions of an integer whose parts are partially distinct, and generalized latin squares. Our method is to generalize Ehrhart's theory of lattice-point counting to a convex polytope dissected by a hyperplane arrangement. We particularly develop the applications to graph and signed-graph coloring, compositions of an integer, and antimagic labellings.