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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Research partially supported by the National Science Foundation and the John Simon Guggenheim Foundation.
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Hanlon, P. A note on the homology of signed posets. J Algebr Comb 5, 245–250 (1996). https://doi.org/10.1007/BF00243788
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DOI: https://doi.org/10.1007/BF00243788