Generating coefficients of representation polynomials

摘要

K. Johnson [6] defines a representation as an equivalence class of order preserving mappings f:X-R from a poset X into the real numbers R. If Cn is a chain of length n then any mapping onto Cn is called an n-valued representation. A representation polynomial p(X,z) is defined asp(X,z)=Σ a(X,i)zⁱwhere a(X,i) is the number of i^th valued representations of the poset X. In this paper a new algorithm to calculate the coefficients a(X,i) is presented.