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Everything about Partially ordered set
Mathematical set with an ordering
In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The word partial is used to indicate that not every pair of elements needs to be comparable; that is, there may be pairs for which neither element precedes the other. Partial orders thus generalize total orders, in which every pair is comparable. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Partially ordered setA 5-minute orientation
- Skim a recent paper: Energy poverty as capacity deprivation: A study of social housing using the partially ordered setInfluential work since 2022
- Pick up a classic book: Mathematical tools for data miningThe most-reprinted book on the subject
- Read the landmark paper: Some partitions associated with a partially ordered setCited 109 times
- Go sideways: Glossary of order theoryA closely related topic
- Go sideways: Total orderA closely related topic
📖 Definitions
Noun A set that has a given, elsewhere specified partial order.
Noun The ordered pair comprising a set and its partial order.
🏆 Landmark papers (most cited)
Some partitions associated with a partially ordered set
On chain and antichain families of a partially ordered set
The spectrum of a ring as a partially ordered set
Average height in a partially ordered set
Records in a Partially Ordered Set
On partitions of a partially ordered set
On the Möbius algebra of a partially ordered set
A partially ordered set and q-Krawtchouk polynomials
🆕 Influential since 2022
Energy poverty as capacity deprivation: A study of social housing using the partially ordered set
Analysis of the multidimensional energy poverty in Italy using the partially ordered set
Special Relationship among Decision Making Units based on Partially Ordered Set and New Evaluation and Projection Methods
Dynamic Programs on Partially Ordered Sets
Stable allocations and partially ordered sets
📚 Books worth reading
Mathematical tools for data miningDan A. Simovici · 2008
Basic posetsJoseph Neggers, Hee Sik Kim · 1998- 📕Fence MethodsJiming Jiang, Thuan Nguyen · 2015
Multi-indicator Systems and Modelling in Partial OrderRainer Brüggemann, Lars Carlsen · 2013
From Objects To Diagrams For Ranges Of FunctorsFriedrich Wehrung · 2011
Topics in spatial stochastic processesSummer School on Spatial Stochastic Processes (2001 Martina Franca, Italy), Vincenzo Capasso · 2003
Combinatorics And Partially Ordered SetsWilliam T. Trotter · 1992
Combinatorics and Partially Ordered SetsWilliam T. Trotter · 1992
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Glossary of order theory Look up Appendix:Glossary of order theory in Wiktionary, the free dictionary. This is a glossary of some terms used in various branches of mathematics…
- Total order In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation…
- Order theory Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing…
- Weak ordering In order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with…
- Preorder In mathematics, in particular in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant…
- Szpilrajn extension theorem In order theory, the Szpilrajn extension theorem (also called the order-extension principle), proved by Edward Szpilrajn in 1930, states that every partial…
- Directed set In mathematics, a directed set (or a directed preorder or a filtered set) is a preordered set in which every finite subset has an upper bound. In other…
- Subset In mathematics, a set A is a subset of a set B if and only if all elements of A are also elements of B; B is then a superset of A. It is possible for A…