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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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.


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.
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References in periodicals archive ?
In the present study, a strong S-box is created with the help of coset graph for the action of modular group and a bijective map. According to our information, this is the first use of coset graphs in the construction of S-box.
In this paper, we establish a novel technique to construct substitution boxes by coset diagrams and bijective maps.
Since g is also a bijective map g(y) = x for all y [member of] Y satisfying the conditions:
The first two transformations are clearly bijective maps in [C.sup.3] that take the interval [a, b] onto [a, b].
Then there exists a bijective map from [LAMBDA] to X which maps [LAMBDA]-closed sets in [LAMBDA] to closed nowhere dense sets in X.
I claim that h is a bijective map on (1) B(a, [r.sub.a]) and (2) B (a, [r.sub.a]) [intersection] [[bar.H].sub.aa'], into B (a', [r.sub.a]) and B (a', [r.sub.a]) [intersection] [[bar.H].sub.a'a] respectively.
A shifted standard Young tableau is a bijective map T: [SD.sub.[lambda]] [right arrow] {1, ..., [absolute value of S[D.sub.[lambda]]]} which is increasing along rows and down columns, i.e.
(2) [[phi].sub.2]: [c,1] [right arrow] [0, 1], strictly monotone decreasingC'bijective map [[phi].sub.2],[[phi].sup.-1.sub.2] are absolutely continuous
Since g is also bijective map g(y) = x for all y [member of] Y satisfying the conditions:
Hence, we have a bijective map [f.sup.-1] : Y [right arrow] X which is an isomorphism from K to H.
Hua's fundamental theorem of geometry of matrices describes the general form of bijective maps on the space of all m X n matrices over a division ring D that preserve adjacency in both directions, explains Semrl.