Hokkaido University Preprint Series in Mathematics
We say that a Cohen-Macaulay poset (partially ordered set) is "superior" if euery open intenrnl ( x , y) of P "' with µp.-.(x,y) :it: 0 is doubly Cohen-Macaulay. For e2-rnmple, if L = P "' is a modular lattice, then the Cohen-Macaulay poset P is superior. We present a formula for the computation of the Cohen-Macaulay type of the Stanley-Reisner ring of the order compleH of a Cohen-Macaulay poset which is superior.