Results in enumeration and topology of interval orders.

摘要

An interval order is an ordered set whose elements are in correspondence with a collection of intervals in a linearly ordered set, with disjoint intervals ordered by their relative position. The order complex of an ordered set is the simplicial complex with vertices corresponding to elements in the ordered set, and k-faces corresponding to (k + 1)-chains. I show that the order complex of any interval order is shellable.; An interval order of length n has elements in correspondence with a collection of intervals in an n element linearly ordered set. A basic interval order of length n has the propertly that removal of any element yields an order of length less than n. I construct and ennumerate the set of basic length n interval orders.