The worst way to collapse a simplex

In general a contractible simplicial complex need not be collapsible. Moreover, there exist complexes which are collapsible but even so admit collapsing sequence where one “gets stuck”, that is can choose the collapses in such way arrives at nontrivial admits no moves. Here we examine this phenomenon case of simplex. particular, characterize all values n and d n-simplex may collapse to d-complex from further possible. Equivalently, language high-dimensional generalizations trees, construct hypertrees anticollapsible,