Finite Posets Simple Step-by-step On The Same Homology Group

This paper mainly studies the steply simplicial cohomology groups of finite partially ordered sets.We will discuss the relationship between this kind of groups and the usual simplicial cohomology groups.We have proved that some special double steply simplicial cohomology groups of finite partially ordered sets are isomorphic to the usual simplicial cohomology groups.Explictly, if P is a finite partially ordered set, d is the sum of all the elements in P, x is an element in P(for all x ∈ P), d₁ is the sum of all the elements, except x, in P, then H_d1H_x(P) is isomorphic to H_d(P) and P is cyclic if and only if H_xH_d1 (P) = 0.