# bijection

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Related to Bijections: Injective

## bi·jec·tion

(bī-jĕk′shən)
n. Mathematics
A function that is both one-to-one and onto.

## bijection

(baɪˈdʒɛkʃən)
n
(Mathematics) a mathematical function or mapping that is both an injection and a surjection and therefore has an inverse. See also injection5, surjection
Translations
bijekce
bijektio
bijection
bijekcija
bijectie
bijektion
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References in periodicals archive ?
In fact, for each group G, there is a universal inverse semigroup S(G), nowadays known as Exel's semigroup, which associates to each partial action of G on a set (topological space) X, a morphism of semigroups between S(G) and the inverse semigroup of partially defined bijections (homeomorphisms) in X.
2013b), Nadeau (2011), Steingrimsson and Williams (2007), and the previous bijections with permutations were extended to bijections with signed permutations.
Also, we present constructive bijections between the set of Motzkin paths of length n - 1 and the sets of irreducible permutations of length n (respectively fixed point free irreducible involutions of length 2n) avoiding a pattern [alpha] for [alpha] [member of] {132, 213, 321}.
BORED with separating sets of numbers into piles of bijections and Cayleigh tables, this weekend, I took to rummaging through a seldom opened cupboard.
The set SYM(G,*) = SYM(G) of all bijections in G forms a group called the permutation (symmetric) group of G.
Morphisms between A-weighted sets are weight preserving bijections.
From the presented details it does not follow that Bohr's complementarity principle is wrong, we have just explicitly reformulated the principle providing strict definitions for which way claims as bijections, and have clarified the useful terms self-interference and cross-interference.
Moreover, there is only one interval-preserving bijection (namely transposition), compared to an indefinitely large number of bijections (of which inversion is one) that do not preserve intervals.
We give recursive bijections between these permutations and certain families of Catalan paths.
An enriched monad T = (T, [eta], [mu]) on an enriched category C is a double exponential monad with respect to an object A provided TX is a double exponential AaX, naturally in X, and under the bijections that this establishes the unit t/x is mapped to the identity natural transformation on C(_ x X, A) and the natural transformation C(_, [[mu].
Note that the bijections used in the proof of the prior theorem preserve the number of occurrences of each letter and hence show the strong equivalence.
The set I (X) is a semigroup where the product of two such bijections is just composition, defined where it makes sense.

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