We consider a simplicial complex generaliztion 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.
The $K_{n+5}$ and $K_{3^2,1^n}$ families are obstructions to $n$-apex
The length polyhedron of an interval order
Interval orders, semiorders and ordered groups
![QR code for arXiv:math/9707216 [math.CO]](http://oss.arxitics.com/images/favicon.svg)