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Transversal: Combinatorics, Set Theory, Bijection, System of Distinct Representatives, Quotient Map, Group Theory - Softcover

 
9786131152153: Transversal: Combinatorics, Set Theory, Bijection, System of Distinct Representatives, Quotient Map, Group Theory

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In combinatorial mathematics, given a collection C of sets, a transversal is a set containing exactly one element from each member of the collection: it is a section of the quotient map induced by the collection. If the original sets are not disjoint, there are several different definitions. 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. Then the set is also called a system of distinct representatives. A less restrictive definition requires that the transversal just has a non-empty intersection with each member of C.A partial transversal is a set containing at most one element from each member of the collection, or a set with an injection from the set to C.

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Reseña del editor

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In combinatorial mathematics, given a collection C of sets, a transversal is a set containing exactly one element from each member of the collection: it is a section of the quotient map induced by the collection. If the original sets are not disjoint, there are several different definitions. 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. Then the set is also called a system of distinct representatives. A less restrictive definition requires that the transversal just has a non-empty intersection with each member of C.A partial transversal is a set containing at most one element from each member of the collection, or a set with an injection from the set to C.

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