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Everything about Order dimension
Mathematical measure for partial orders
In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the intersection of which gives rise to the partial order. This concept is also sometimes called the order dimension or the Dushnik–Miller dimension of the partial order. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Order dimensionA 5-minute orientation
- Skim a recent paper: Three-dimensional atomic structure and local chemical order of medium- and high-entropy nanoalloysInfluential work since 2022
- Pick up a classic book: Family size and achievementThe most-reprinted book on the subject
- Read the landmark paper: Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder TransitionCited 5,618 times
- Go sideways: Incidence (graph)A closely related topic
- Go sideways: Schnyder's theoremA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
Second-order scalar-tensor field equations in a four-dimensional space
Existence of Long-Range Order in One and Two Dimensions
The Complexity of the Partial Order Dimension Problem
Simplicial complexes: higher-order spectral dimension and dynamics
The order dimension of the complete graph
High-order central Hermite WENO schemes: Dimension-by-dimension moment-based reconstructions
GGS-groups: Order of congruence quotients and Hausdorff dimension
🆕 Influential since 2022
Three-dimensional atomic structure and local chemical order of medium- and high-entropy nanoalloys
Coupling between magnetic order and charge transport in a two-dimensional magnetic semiconductor
Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order
Multiview PCA: A Methodology of Feature Extraction and Dimension Reduction for High-Order Data
Fourth-Order Dimension Preserved Tensor Completion With Temporal Constraint for Missing Traffic Data Imputation
📚 Books worth reading
Family size and achievementJudith Blake · 1989
Extrinsic Geometric FlowsBen Andrews, Bennett Chow · 2020- 📕Monstrous OntologiesCaterina Nirta, Andrea Pavoni · 2021
- 📕The book of purposeCharles Ray Salmon · 1972
- 📕Geometric analysis, mathematical relativity, and nonlinear partial differential equationsSoutheast Geometry Seminar (15th 2009 University of Alabama at Birmingham) · 2013
- 📕Rings with Polynomial Identities and Finite Dimensional Representations of AlgebrasEli Aljadeff, Antonio Giambruno · 2020
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Incidence (graph) In graph theory, a vertex is incident with an edge if the vertex is one of the two vertices the edge connects. An incidence is a pair ( u , e ) {\displaystyle…
- Schnyder's theorem In graph theory, Schnyder's theorem is a characterization of planar graphs in terms of the order dimension of their incidence posets. It is named after…
- Incidence poset In mathematics, an incidence poset or incidence order is a type of partially ordered set that represents the incidence relation between vertices and edges…
- Inclusion order In the mathematical field of order theory, an inclusion order is the partial order that arises as the subset-inclusion relation on some collection of objects…
- 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…
- Semiorder In order theory, a branch of mathematics, a semiorder is a type of ordering for items with numerical scores, where items with widely differing scores are…
- Polytree In mathematics, and more specifically in graph theory, a polytree (also called directed tree, oriented tree or singly connected network) is a directed…
- Series-parallel partial order In order-theoretic mathematics, a series-parallel partial order is a partially ordered set built up from smaller series-parallel partial orders by two…