TY - JOUR
T1 - Monotonicity of the cd-index for polytodes
AU - Billera, Louis J.
AU - Ehrenborg, Richard
PY - 2000/3
Y1 - 2000/3
N2 - We prove that the cd-index of a convex polytope satisfies a strong monotonicity property with respect to the cd-indices of any face and its link. As a consequence, we prove for d-dimensional polytopes a conjecture of Stanley that the cd-index is minimized on the d-dimensional simplex. Moreover, we prove the upper bound theorem for the cd-index, namely that the cd-index of any d-dimensional polytope with n vertices is at most that of C(n, d), the d-dimensional cyclic polytope with n vertices.
AB - We prove that the cd-index of a convex polytope satisfies a strong monotonicity property with respect to the cd-indices of any face and its link. As a consequence, we prove for d-dimensional polytopes a conjecture of Stanley that the cd-index is minimized on the d-dimensional simplex. Moreover, we prove the upper bound theorem for the cd-index, namely that the cd-index of any d-dimensional polytope with n vertices is at most that of C(n, d), the d-dimensional cyclic polytope with n vertices.
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U2 - 10.1007/s002090050480
DO - 10.1007/s002090050480
M3 - Article
AN - SCOPUS:0034147142
SN - 0025-5874
VL - 233
SP - 421
EP - 441
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3
ER -