Everything about Isomorphism
In mathematics, invertible homomorphism
In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them, and this is often denoted as . The word is derived from Ancient Greek ἴσος 'equal' and μορφή 'form, shape'. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: IsomorphismA 5-minute orientation
- Skim a recent paper: Improving Graph Neural Network Expressivity via Subgraph Isomorphism CountingInfluential work since 2022
- Pick up a classic book: AlgebraThe most-reprinted book on the subject
- Read the landmark paper: The Iron Cage Revisited: Institutional Isomorphism and Collective Rationality in Organizational FieldsCited 34,535 times
- Go sideways: Group isomorphismA closely related topic
- Go sideways: HomomorphismA closely related topic
📖 Definitions
Noun Similarity of form the similarity in form of organisms, which may be due to convergent evolution or shared genetic background, e.g. an algae species in which the haploid and diploid life stages are indistinguishable based on morphology. the similarity in the crystal structures of similar chemical compounds. the similarity in the structure or processes of different organizations.
Noun the similarity in form of organisms, which may be due to convergent evolution or shared genetic background, e.g. an algae species in which the haploid and diploid life stages are indistinguishable based on morphology.
Noun the similarity in the crystal structures of similar chemical compounds.
Noun the similarity in the structure or processes of different organizations.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The Iron Cage Revisited: Institutional Isomorphism and Collective Rationality in Organizational Fields
An Algorithm for Subgraph Isomorphism
DOES ISOMORPHISM LEGITIMATE?
A (sub)graph isomorphism algorithm for matching large graphs
Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids
Follow the Leader: Mimetic Isomorphism and Entry Into New Markets
Practical graph isomorphism, II
The Social Construction of Organizational Knowledge: A Study of the Uses of Coercive, Mimetic, and Normative Isomorphism
🆕 Influential since 2022
Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting
Graph isomorphism-based algorithm for cross-checking chemical and crystallographic descriptions
Institutional isomorphism under the test of Non-financial Reporting Directive. Evidence from Italy and Spain
Attention-guided graph isomorphism learning: A multi-task framework for fault diagnosis and remaining useful life prediction
Tailoring the d‐Band Center over Isomorphism Pyrite Catalyst for Optimized Intrinsic Affinity to Intermediates in Lithium–Oxygen Batteries
📚 Books worth reading
AlgebraMichael Artin · 2009
Lectures on the Curry-Howard isomorphismMorten Heine Sørensen · 2006
The computational complexity of equivalence and isomorphism problemsThomas Thierauf · 2000- 📕Variations on dimension subgroupsRobert J. Valenza · 1979
The Isomorphism Problem in Coxeter GroupsPatrick Bahls · 2005- 📕The Curry-Howard isomorphismPhilippe De Groote · 1995
- 📕Teorii͡a︡ izomorfnoĭ smesimostiV. S. Urusov · 1977
A feature-oriented label graph isomorphism algorithm and its applicationsFan, Kuo-Chin 1959- · 1989
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Group isomorphism In abstract algebra, a group isomorphism is a function between two groups that sets up a bijection between the elements of the groups in a way that respects…
- Homomorphism In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector…
- Automorphism In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping…
- Order isomorphism In the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism…
- Quotient group In the branch of mathematics known as group theory, a quotient group or factor group is a group obtained by aggregating similar elements of a larger group…
- Symmetry in mathematics Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object…
- Bijection In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the…
- Equivalent definitions of mathematical structures In mathematics, equivalent definitions are used in two somewhat different ways. First, within a particular mathematical theory (for example, Euclidean…