A linear extension of P is a linear order < on the same ground set X such that x < y whenever x <y. The set of linear extensions is denoted L(P), and we set I(P) ...

We estimate the number of linear extensions of such an ordered set, showing that this number is almost always very close to η(n!)2, where η is a known constant.

Abstract. We study asymptotics of the number of linear extensions of the random Gn,p G n , p partial order, where p p is fixed and n→∞ n → ∞ . In particular, it ...

In order theory, a branch of mathematics, a linear extension of a partial order is a total order (or linear order) that is compatible with the partial order.

Jun 29, 2012 · If you're given a collection of partial orders, topological sort will tell you if there's an extension of the collection to a total order (an ...

x <y. We define a linear extension of a graph G on [ n] to be a linear extension of the corresponding partial order.

Dec 11, 2022 · We model the hierarchy as a partial order so that the lists are random linear extensions. We account for noise via a random queue-jumping ...

Nov 2, 2014 · For example, the linear extensions of the partially ordered set ((1,2),(3,4)) are 1234, 1324, 1342, 3124, 3142, and 3412, all of which have 1 ...

Given a partial order of N N items, a linear extension that is almost uniformly distributed, in the sense of variation distance, is generated.

Apr 3, 2022 · random linear extension of a fixed infinite poset. Our goal is to study order-invariant processes in general. In this talk, I. shall explain ...