Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 463-464 (2004)

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Disjoint faces of complementary dimension

Mike Develin

American Institute of Mathematics, 360 Portage Ave., Palo Alto, CA 94306-2244 USA, e-mail:

Abstract: In this short note, we show that if $P$ is a $d$-polytope which is not the simplex, then for all $0<k<d$, we can find a $k$-face of $P$ and a $(d-k)$-face of $P$ which are disjoint. This statement generalizes a result of Miller and Helm [HM], who proved it for the case $k=1$.

[HM] Helm, D.; Miller, E.: Bass numbers of semigroup-graded local cohomology. Pacific Journal of Math. \textbf{209} (2003), 41--66.

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Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.

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