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.
Oct 19, 2015 · To find linear extensions of your given posets, proceed one element at a time, always picking a minimal element of the poset of the remaining not-yet-chosen ...
A binary relation ! on a set P is defined to be a partial order on P when ! is reflexive, transitive, and antisymmetric. We will refer to the pair (P,!) ...
Nov 5, 2023 · We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent ...
Jul 16, 2024 · In this paper we give a broad survey of inequalities for the number of linear extensions of finite posets, both as a function of the poset and ...
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Mar 19, 2022 · A linear order L on X is called a linear extension (also, a topological sort ) of P, if x<y in L whenever x<y in P. For example, the table ...
Let (E, ~) be a finite poset of cardinality n, and s be a linear extension of B. We call allowed permutation on s a permutation 7T of [n] such that So7T is a ...
Feb 14, 2022 · The study of linear extensions of finite posets is surprisingly rich as they generalize per- mutations, combinations, standard Young ...
We show how to extend this idea to a certain class of infinite posets, and show that fundamental correlation inequalities for finite posets hold in the infinite ...
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A linear extension of a finite poset P of size n is a total ordering of its elements such that i < j whenever π i < π j in the poset P.