扩充欧空间中单纯复形的一个计数问题

A Count Problem of Simplicial Complex in Euclidean Space

通过推广平图和圈的概念,给出平复形的概念.证明m=3时,对于具有a0个顶点的极大平复形K,其3维单形的个数为3a0-10;2维单形的个数为6a0-20;1维单形的个数为4a0-10;并猜想m≥2时,对于极大平复形K,其m维单形的个数为m(a0-m-1)+2.

A popularization in the concept of planar graph and cycle will be carried out to yield the concept of planar complex. We prove that when m = 3 , the number of 3-dimension simplex is 3a0-10 for maximal planar complex K ; the number of 2-dimension is 6a0-20 and the number of 1-dimension is 4a0-10. And we guess that when m ≥ 2, the number of m -dimension simplex is m（a0-m-1 ） ＋ 2 for maximal planar complex K.