A Solution to the Generalized Cevian Problem Using Forest Polynomials

摘要

In this paper, we examine the effect of dissecting an n-dimensional simplex using cevians (cross-sections passing through n - 1 of the vertices of the simplex). We describe a formula for the number of pieces the simplex is dissected into using a polynomial involving only the number of each type of cevian. The polynomial in question involving terms involving the edges of the simplex, but discarding those terms involving cycles of the underlying graph. Thus, we call such a polynomial a "forest polynomial."