Transversal (combinatorics)
In mathematics, particularly in combinatorics, given a family of sets, here called a collection C, a transversal (also called a cross-section) is a set containing exactly one element from each member of the collection. When the sets of the collection are mutually disjoint, each element of the transversal corresponds to exactly one member of C (the set it is a member of). If the original sets are not disjoint, there are two possibilities for the definition of a transversal:
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- enIn mathematics, particularly in combinatorics, given a family of sets, here called a collection C, a transversal (also called a cross-section) is a set containing exactly one element from each member of the collection. When the sets of the collection are mutually disjoint, each element of the transversal corresponds to exactly one member of C (the set it is a member of). If the original sets are not disjoint, there are two possibilities for the definition of a transversal:
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- enIn mathematics, particularly in combinatorics, given a family of sets, here called a collection C, a transversal (also called a cross-section) is a set containing exactly one element from each member of the collection. When the sets of the collection are mutually disjoint, each element of the transversal corresponds to exactly one member of C (the set it is a member of). If the original sets are not disjoint, there are two possibilities for the definition of a transversal: * One variation is that there is a bijection f from the transversal to C such that x is an element of f(x) for each x in the transversal. In this case, the transversal is also called a system of distinct representatives (SDR). * The other, less commonly used, does not require a one-to-one relation between the elements of the transversal and the sets of C. In this situation, the members of the system of representatives are not necessarily distinct. In computer science, computing transversals is useful in several application domains, with the input family of sets often being described as a hypergraph.
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- Transversal (combinatorics)
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- enTransversal (combinatorics)
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- Axiom of choice
- Bernstein set
- Bijection
- Bipartite graph
- Blocking set
- Category:Combinatorics
- Category:Families of sets
- Category:Group theory
- Category theory
- Codomain
- Combinatorics
- Computational complexity
- Computer science
- Coset
- Direct product of groups
- Domain of a function
- Enumeration algorithm
- Equivalence class
- Equivalence relation
- Eugene Lawler
- Family of sets
- Full transformation semigroup
- Group theory
- H. J. Ryser
- Hall's marriage theorem
- Hypergraph
- Image (mathematics)
- Independent set (graph theory)
- Inverse element
- Kernel (set theory)
- Leon Mirsky
- Mathematics
- Matroid
- Partition of a set
- Perfect matching
- Perfect set
- Permanent (mathematics)
- Polish space
- Projective plane
- Quotient map
- Rainbow-independent set
- Regular semigroup
- Section (category theory)
- Set (mathematics)
- Subgroup
- Vertex cover in hypergraphs
- SameAs
- 25zc9
- m.03mwhb
- Q2208651
- Querschnitt (Mathematik)
- Transversal (matemática)
- Transwersala
- Трансверсаль
- Subject
- Category:Combinatorics
- Category:Families of sets
- Category:Group theory
- WasDerivedFrom
- Transversal (combinatorics)?oldid=1106927379&ns=0
- WikiPageLength
- 12224
- Wikipage page ID
- 897733
- Wikipage revision ID
- 1106927379
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