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A poset which is shellable but not lexicographically shellable. (English) Zbl 0579.06001

For those interested in shellability questions the example provided in this paper is that of a regular CW-complex which is not shellable, but whose barycentric subdivision is shellable. This is one of several recent important examples showing that shellable posets need not be lexicographically shellable. The author provides a decomposition of \(K=[0,4]^ 3\) into the union of three maximal cells whose pairwise intersections are disconnected and whose barycentric subdivision admits a shelling obtained after a computer search and which is not presented in the (short) paper under review. Altogether the approach described constitutes an interesting blend of theory, geometric tailoring and an application of the computer to replace and in some way improve upon mere pencil-and-paper efforts subject to the pains and errors thereof.

MSC:

06A06 Partial orders, general
52Bxx Polytopes and polyhedra
57Q05 General topology of complexes
55U10 Simplicial sets and complexes in algebraic topology
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References:

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[2] Björner, A., Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc., 260, 159-183 (1980) · Zbl 0441.06002
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[6] A. Vince, M. Wachs: A shellable poset that is not lexicographically shellable, Combinatorrca, to appear.; A. Vince, M. Wachs: A shellable poset that is not lexicographically shellable, Combinatorrca, to appear. · Zbl 0623.06003
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