n维超长方体中图形函数的计数

The Counting of Graphical Functions in n-Dimensional Super-Cuboids

利用组合几何计数原理和方法,研究在均匀分割的n维超长方体中,所有n维超长方体的任一k维测度和的计数问题.从顶点和、周长和、面积和等低维测度和计数方法入手,然后类比迁移到高维空间中,最终得到任一k维测度和的计数公式,并在五种特殊n维超长方体中推广.

By means of the principles and methods of combinatorial geometric counting, the enumeration problems of the total measures for any k-dimension of n-dimensional super-cuboids under uniform partition are studied. It starts from the enumeration methods of low dimensional total measures, such as vertices summation, perimeter and total area, then compares and transfers the methods to higher dimensional space. Finally, it gets the enumeration formula for the total measures of any k-dimension of the super-cuboids, and promotes into five special kinds of n-di- mensional super-cuboids.