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A mapping ƒ from a set A onto a set B which is both an injection and a surjection; that is, for every element b of B there is a unique element a of A for which ƒ (a) = b. Also known as bijective mapping.


A function is bijective or a bijection or a one-to-one correspondence if it is both injective (no two values map to the same value) and surjective (for every element of the codomain there is some element of the domain which maps to it). I.e. there is exactly one element of the domain which maps to each element of the codomain.

For a general bijection f from the set A to the set B:

f'(f(a)) = a where a is in A and f(f'(b)) = b where b is in B.

A and B could be disjoint sets.

See also injection, surjection, isomorphism, permutation.
References in periodicals archive ?
4 Let G = G(V, E) be a simple graph with [absolute value of V] = n and consider a bijection f [member of] Bij(V, [n]).
In this section we introduce a rotation map tc on the positions in the word Qc, and naturally extend it to a map on almost positive roots and cluster variables using the bijections of Section 2.
It is straightforward to check that the restriction of the Robinson-Schensted correspondence to these words is a bijection to standard Young tableaux such that the weight of the word is mapped to the shape of the tableau.
There is a simple bijection between reduced words of a Grassmannian permutation [sigma] and standard Young tableaux of a shape determined by [sigma].
A bijection for triangulations, quadrangulations, pentagulations, etc.
In Section 5 we present the main result, about the number of d-cycles in G(n, 312) and subsequently give a bijection that proves this, in Sections 6 and 7.
H]) of all Smarandache bijections (S-bijections) in [G.
What is more the wavefunctions were "traced" in time in order for one to prove possible bijections.
A tabloid is a bijection T: [lambda] [right arrow] {1, .
The set SYM(G, *) = SY M(G) of all bijections in a groupoid (G, *) forms a group called the permutation (symmetric) group of the groupoid (G, *).
The present paper intends to be a summarized overview of both bijections of Section 3 and 4.
The set SY M (L, *) = SY M (L) of all bijections in a groupoid (L, *) forms a group called the permutation (symmetric) group of the groupoid (L, *).