A Study About Stanly's Problem Of Acyclic Digraph

Acyclic digraph has much practical value,many problem are efficiently solved by its graph models. This paper gives special attention to some properties of acyclic digraph, in fact,it took much energy to tackle the problem that whether closure matrix and reduced matrix are similar for a given acyclic digraph. Some journals do the same work for the similarity between cover matrix and incidence matrix of a poset. This problem is firstly stated by stanly. Stanly asks if there is any reasonable criterion for determine when two elements of the incidence algebra of a poset are conjugate.It's called Stanly's problem. We have done much work about Stanly's problem,and given two algebra formulars which can be used to compute another matrix when one matrix is known. It is convient for us to compute one from another by computer. Concretely, we make positive answers for three conditions:directed interval graph,acyclic digraph whose adjcent matrix is eche lon matrix,the face lattice of a polytope in three-dimensional space.Finally we introduce the results from numeric experiments by computer.And we give a general way to construct counter examples.