Abstract
A new index for convex polytopes is introduced. It is a vector whose length is the dimension of the linear span of the flag vectors of polytopes. The existence of this index is equivalent to the generalized Dehn-Sommerville equations. It can be computed via a shelling of the polytope. The ranks of the middle perversity intersection homology of the associated toric variety are computed from the index. This gives a proof of a result of Kalai on the relationship between the Betti numbers of a polytope and those of its dual.
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Margaret M. Bayer was supported in part by a National Science Foundation grant, by a Northeastern University Junior Research Fellowship, and by the Institute for Mathematics and Its Applications.
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Bayer, M.M., Klapper, A. A new index for polytopes. Discrete Comput Geom 6, 33–47 (1991). https://doi.org/10.1007/BF02574672
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DOI: https://doi.org/10.1007/BF02574672