TY - JOUR

T1 - A Simple Proof of the Upper Bound Theorem

AU - Alon, N.

AU - Kalai, G.

PY - 1985

Y1 - 1985

N2 - Let ci(n, d) be the number of i-dimensional faces of a cyclic d-polytope on n vertices. We present a simple new proof of the upper bound theorem for convex polytopes, which asserts that the number of i-dimensional faces of any d-polytope on n vertices is at most ci(n, d). Our proof applies for arbitrary shellable triangulations of (d−1) spheres. Our method provides also a simple proof of the upper bound theorem for d-representable complexes.

AB - Let ci(n, d) be the number of i-dimensional faces of a cyclic d-polytope on n vertices. We present a simple new proof of the upper bound theorem for convex polytopes, which asserts that the number of i-dimensional faces of any d-polytope on n vertices is at most ci(n, d). Our proof applies for arbitrary shellable triangulations of (d−1) spheres. Our method provides also a simple proof of the upper bound theorem for d-representable complexes.

UR - http://www.scopus.com/inward/record.url?scp=85016174015&partnerID=8YFLogxK

U2 - 10.1016/S0195-6698(85)80029-9

DO - 10.1016/S0195-6698(85)80029-9

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AN - SCOPUS:85016174015

SN - 0195-6698

VL - 6

SP - 211

EP - 214

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 3

ER -