19: Partially ordered sets

Elementary Foundations: An Introduction to Topics in Discrete Mathematics · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under GNU Free Documentation, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    • 19.1: Motivation
      In many of the sets we encounter, there is some notion of elements being “less than or equal to” other elements in the set.
    • 19.2: Definition and properties
      Notice that in each of the examples in Section 19.1, the notion of “is smaller than” is defined via a relation.
    • 19.3: Graph for a partial order
      Hasse diagram: a diagram for the graph for a partial order on a finite set A, omitting reflexive loops and transitive “composite” edges, and placing “smaller” elements lower on the diagram instead of using arrows
    • 19.4: Total Orders
      Comparable Elements: elements a,b in a partially ordered set such that either a⪯b or b⪯a
    • 19.5: Maximal/minimal Elements
      Each of the following definitions are for a subset B of a partially ordered set A.
    • 19.6: Topological Sorting
      Sometimes we want to turn a partial order into a total order. What makes an order partial instead of total is the presence of pairs of incomparable elements.
    • 19.7: Activities
    • 19.8: Exercises

    This page titled 19: Partially ordered sets was last modified on Tue, 01 Sep 2026 03:33:55 GMT and is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Jeremy Sylvestre via source content that was edited to the style and standards of the LibreTexts platform.