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Bagchi, Bhaskar and Datta, Basudeb (2013) ON POLYTOPAL UPPER BOUND SPHERES. In: MATHEMATIKA, 59 (2). pp. 493-496.

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Official URL: http://dx.doi.org/10.1112/S0025579313000016


Generalizing a result (the case k = 1) due to M. A. Perles, we show that any polytopal upper bound sphere of odd dimension 2k + 1 belongs to the generalized Walkup class K-k(2k + 1), i.e., all its vertex links are k-stacked spheres. This is surprising since it is far from obvious that the vertex links of polytopal upper bound spheres should have any special combinatorial structure. It has been conjectured that for d not equal 2k + 1, all (k + 1)-neighborly members of the class K-k(d) are tight. The result of this paper shows that the hypothesis d not equal 2k + 1 is essential for every value of k >= 1.

Item Type: Journal Article
Additional Information: copyright for this article belongs to LONDON MATH SOC,ENGLAND
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 28 Dec 2013 06:19
Last Modified: 28 Dec 2013 06:24
URI: http://eprints.iisc.ac.in/id/eprint/47990

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