Hyperplane arrangements and interval orders
by
Richard Stanley
MIT

Let P be a set of closed intervals [a, b] on the real line. Define [a, b] < [c, d] if b < c. Then P becomes a partially ordered set called an interval order. There is a close connection between interval orders and the theory of hyperplane arrangements. For instance, the nonisomorphic labelled interval orders that can arise from n labelled intervals of length one are in one-to-one correspondence with the regions of the arrangement x_i-x_j=-1, 1, for 1 <= i < j <= n, in Rⁿ. We will survey the basic connections between interval orders and hyperplane arrangements and give some applications to the enumeration of interval orders.

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Date received: June 3, 1999