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The width of five-dimensional prismatoids

Abstract: Santos' construction of counter-examples to the Hirsch Conjecture (2012) is based on the existence of prismatoids of dimension d of width greater than d. Santos, Stephen and Thomas (2012) have shown that this cannot occur in d ? 4. Motivated by this, we here study the width xf five-dimensional prismatoids, obtaining the following results: (i) There are 5-prismatoids of width 6 with only 25 vertices versus the 48 vertices in Santos' original construction. This leads to non-Hirsch polytopes of dimension 20, rather than the original dimension 43. (ii) There are 5-prismatoids with n vertices and width ?(?n) for arbitrarily large n. Hence, the width of 5-prismatoids is unbounded. Both constructions, in particular that of a twenty-dimensional non-Hirsch polytope, are totally explicit.

 Fuente: Proceedings of the London Mathematical Society, Vol. 110, Iss. 3, 647-672 (2015)

Editorial: London Mathematical Society

 Fecha de publicación: 01/03/2015

Nº de páginas: 26

Tipo de publicación: Artículo de Revista

 DOI: 10.1112/plms/pdu064

ISSN: 0024-6115,1460-244X

Proyecto español: MTM2008-04699-C03-02 ; MTM2011-22792 ; CSD2006-00032 (i-MATH)

Url de la publicación: https://doi.org/10.1112/plms/pdu064