Journal of Combinatorics
Volume 3 (2012)
Limits of interval orders and semiorders
Pages: 163 – 183
We study poset limits given by sequences of finite interval orders or, as a special case, finite semiorders. In the interval order case, we show that every such limit can be represented by a probability measure on the space of closed subintervals of [0, 1], and we define a subset of such measures that yield a unique representation. In the semiorder case, we similarly find unique representations by a class of distribution functions.