Series-parallel partial order

In <a href="/facts/Order_theory/gn6fM3oJ">order-theoretic</a> mathematics, a series-parallel partial order is a <a href="/facts/Partially_ordered_set/qb4a3FAX">partially ordered set</a> built up from smaller series-parallel partial orders by two simple composition operations.
The series-parallel partial orders may be characterized as the N-free finite partial orders; they have <a href="/facts/Order_dimension/JaFXu3WE">order dimension</a> at most two. They include <a href="/facts/Weak_order/LmaM9lSs">weak orders</a> and the <a href="/facts/Reachability/D8cQpSFQ">reachability</a> relationship in <a href="/facts/Tree_(graph_theory)/TCWk4Joy">directed trees</a> and directed <a href="/facts/Series%E2%80%93parallel_graph/XdfWgomL">series–parallel graphs</a>. The <a href="/facts/Comparability_graph/dLht35EJ">comparability graphs</a> of series-parallel partial orders are <a href="/facts/Cograph/c3lYz8fV">cographs</a>.
Series-parallel partial orders have been applied in <a href="/facts/Job_shop_scheduling/1JjAvD3m">job shop scheduling</a>, <a href="/facts/Machine_learning/e0w0XJTu">machine learning</a> of event sequencing in <a href="/facts/Time_series/fSXPR817">time series</a> data, transmission sequencing of <a href="/facts/Multimedia/PtJteq27">multimedia</a> data, and throughput maximization in <a href="/facts/Dataflow_programming/60IdWpE1">dataflow programming</a>.
Series-parallel partial orders have also been called multitrees; however, that name is ambiguous: <a href="/facts/Multitree/xK7npdzB">multitrees</a> also refer to partial orders with no four-element diamond suborder and to other structures formed from multiple trees.

Series-parallel partial order open-in-new

Series-parallel partial order