58 research outputs found
f-vectors implying vertex decomposability
We prove that if a pure simplicial complex of dimension d with n facets has
the least possible number of (d-1)-dimensional faces among all complexes with n
faces of dimension d, then it is vertex decomposable. This answers a question
of J. Herzog and T. Hibi. In fact we prove a generalization of their theorem
using combinatorial methods
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