Michelle Wachs

Abstract: We consider a simplicial complex generalization of a result of Billera and Meyers that every nonshellable poset contains the smallest nonshellable poset as an induced subposet. We prove that every nonshellable 2-dimensional simplicial complex contains a nonshellable induced subcomplex with less than 8 vertices. We also establish CL-shellability of interval orders and as a consequence obtain a formula for the Betti numbers of any interval order.

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