(redirected from Bijections)
Also found in: Dictionary.
Related to Bijections: Injective


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 ?
A few remarks are pertinent about the previous definition: Firstly the axiom (i) reflects the fact that the neutral element of the group acts as the identity while the axioms (ii) and (iii) combined say that the composition of bijections indexed by elements of the group, wherever it is defined, is compatible with the operation of the group.
For the first one, through bijections, we give relations between the number of corners in permutation tableaux, alternative tableaux and tree-like tableaux.
For the sets counted by the Motzkin numbers, we exhibit bijections between them and the set of Motzkin paths.
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.
Sets a, d, f, and i are all transpositionally equivalent, given the bijections a [right arrow] d [right arrow] f [right arrow] i tabulated in Example 3.
In Section 4 we use our decompositions to give recursive bijections between the set of even threads of length n and the set of Catalan paths of length n + 1 with no ascent of length two, and between the set of odd threads of length n and the set of Catalan paths of length n with no four consecutive steps NEEN.
X]) is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], up to the bijections established.
We will show the first equivalence by constructing a bijection f between [A.
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, *).
We then use the observation to define the structure of the p-avoiding inversion sequences and relate them to equinumerous combinatorial families via bijections, recurrences or generating functions.
7: for all V [member of] div and G [member of] 1-grp, there are natural inverse bijections