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What (who) is matching theorem - definition
THEOREM
Hall marriage theorem; Marriage Theorem; Hall theorem; Set of distinct representatives; Hall's perfect matching theorem
Bracket matching
A SYNTAX HIGHLIGHTING FEATURE OF CERTAIN TEXT EDITORS AND INTEGRATED DEVELOPMENT ENVIRONMENTS THAT HIGHLIGHTS MATCHING PAIRS OF BRACKETS.
Braces matching; Brace matching
Bracket matching, also known as brace matching or parentheses matching, is a syntax highlighting feature of certain text editors and integrated development environments that highlights matching sets of brackets (square brackets, curly brackets, or parentheses) in languages such as Java, JavaScript, and C++ that use them. The purpose is to help the programmer navigate through the code and also spot any improper matching, which would cause the program to not compile or malfunction.
Matching theory (economics)
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SEARCH THEORY
Search and matching theory; Matching function; Matching Function; Matching model; Job matching; Search and matching; Matching theory (macroeconomics); Matching market; Matching theory (economics)
In economics, matching theory, also known as search and matching theory, is a mathematical framework attempting to describe the formation of mutually beneficial relationships over time.
Search and matching theory (economics)
SEARCH THEORY
Search and matching theory; Matching function; Matching Function; Matching model; Job matching; Search and matching; Matching theory (macroeconomics); Matching market; Matching theory (economics)
In economics, search and matching theory, is a mathematical framework attempting to describe the formation of mutually beneficial relationships over time. It is closely related to stable matching theory.
Wikipedia
Hall's marriage theorem
In mathematics, Hall's marriage theorem, proved by Philip Hall (1935), is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and sufficient condition for an object to exist:
- The combinatorial formulation answers whether a finite collection of sets has a transversal—that is, whether an element can be chosen from each set without repetition. Hall's condition is that for any group of sets from the collection, the total unique elements they contain is at least as large as the number of sets in the group.
- The graph theoretic formulation answers whether a finite bipartite graph has a perfect matching—that is, a way to match each vertex from one group uniquely to a vertex from the other group. Hall's condition is that any subset of vertices from one group has a neighbourhood of equal or greater size.
