Representation functions and the Neggers-Stanley condition for weight-shaped-posets

We introduce the class of weight-shaped-posets and we define the representation functions of such ws-posets as generalizations of the representation polynomials of finite posets. We define the Brylawski decomposition of ws-posets and use it to construct the algorithm for the computation of the representation functions. The class of ws-posets contains a class of fuzzy posets for example. The Neggers-Stanley conjecture for ws-posets is also discussed. (c) 2008 Elsevier Ltd. All rights reserved