Limits of interval orders and semiorders

TL;DR

This paper investigates the limits of sequences of finite interval orders and semiorders, providing unique representations via probability measures and distribution functions, advancing the understanding of their asymptotic behavior.

Contribution

It establishes a framework for representing limits of interval orders and semiorders with unique measures and functions, clarifying their structural properties.

Findings

Every interval order limit can be represented by a probability measure on closed subintervals of [0,1]

Semiorder limits have unique representations via specific distribution functions

The paper characterizes the subset of measures that yield unique representations

Abstract

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.