The Lefschetz Property for Barycentric Subdivisions of Shellable Complexes
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چکیده
We show that an ’almost strong Lefschetz’ property holds for the barycentric subdivision of a shellable complex. From this we conclude that for the barycentric subdivision of a CohenMacaulay complex, the h-vector is unimodal, peaks in its middle degree (one of them if the dimension of the complex is even), and that its g-vector is an M -sequence. In particular, the (combinatorial) g-conjecture is verified for barycentric subdivisions of homology spheres. In addition, using the above algebraic result, we derive new inequalities on a refinement of the Eulerian statistics on permutations, where permutations are grouped by the number of descents and the image of 1.
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Preprints (4 Total)
We prove that the (d − 2)-nd barycentric subdivision of every convex d-ball is shellable. This yields a new characterization of the PL property in terms of shellability: A sphere or a ball is PL if and only if it becomes shellable after sufficiently many barycentric subdivisions. This improves results by Whitehead, Zeeman and Glaser. Moreover, we show the Zeeman conjecture is equivalent to the ...
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تاریخ انتشار 2008