Let us call a sequence of numbers heapable if they can be sequentially
inserted to form a binary tree with the heap property, where each insertion
subsequent to the first occurs at a leaf of the tree, i.e. below a previously
placed number. In this paper we consider a variety of problems related to
heapable sequences and subsequences that do not appear to have been studied
previously. Our motivation for introducing these concepts is two-fold. First,
such problems correspond to natural extensions of the well-known secretary
problem for hiring an organization with a hierarchical structure.