Abstract
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].
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References
H. Cartan and S. Eilenberg,Homological Algebra,Oxford University Press, Oxford,1956.
S. Fischer,”Signed poset homology and q-analog Mobius functions,”preprint.
P.J. Hilton and U. Stammbach,A Course in Homological Algebra,Springer Graduate Texts in Mathematics, Springer-Verlag,1971.
V. Reiner,”Signed posets,”JCTA 62(2)(1993),324–360.
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Hanlon, P. A Note on the Homology of Signed Posets. Journal of Algebraic Combinatorics 5, 245–250 (1996). https://doi.org/10.1023/A:1022428328476
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DOI: https://doi.org/10.1023/A:1022428328476