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Home > Vol 5, No 3 (1996)

Phil Hanlon

Let S be a signed poset in the sense of Reiner [4]. Fischer [2] defines the homology of S, in terms of a partial ordering P( S) associated to S, to be the homology of a certain subcomplex of the chain complex of P( S). In this paper we show that if P( S) is Cohen-Macaulay and S has rank n, then the homology of S vanishes for degrees outside the interval [ n/2, n].

1. H. Cartan and S. Eilenberg, Homological Algebra, Oxford University Press, Oxford, 1956.
2. S. Fischer, "Signed poset homology and q-analog Mobius functions," preprint.
3. P.J. Hilton and U. Stammbach, A Course in Homological Algebra, Springer Graduate Texts in Mathematics, Springer-Verlag, 1971.
4. V. Reiner, "Signed posets," JCTA 62(2) (1993), 324-360.