On the Homology of Distributive Lattices

This paper gives a method for computing the reduced poset homology of the rank-selected subposet of a distributive lattice. As an example of the method, letLbe the lattice [a + 1] × ··· × [a + 1] (b-times).Sbacts onLby permuting coordinates. ForS⊇ [ab], we give a description of the decomposition of the reduced homology ofLSas anSb-module. This generalizes L. Solomonʹs result for decomposition of the reduced homology of the Boolean algebra (Bb)Sas anSb-module.