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n. Mathematics
A function that is both one-to-one and onto.

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.


(Mathematics) a mathematical function or mapping that is both an injection and a surjection and therefore has an inverse. See also injection5, surjection
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
References in periodicals archive ?
We show that [THETA] and [PHI] are mutually inverse bijections. Due to symmetry, it suffices to show that [THETA]([PHI](I)) = I for any I [member of] Id(S).
Let it be A = (P, L, I) an affine plane and S = {[psi]: P [right arrow] P| where [psi]--is bijection} set of bijections to set points P on yourself.
We use extensively the bijections [[psi].sub.n] and [[??].sub.n] between [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the bijections [[PHI].sub.n] and [[??].sub.n] between [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], studied in [4] (see Appendix for more information).
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.
For the first one, through bijections, we give relations between the number of corners in permutation tableaux, alternative tableaux and tree-like tableaux.
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}.
Our general approach is to merge several steps of each round function of SHARK into table lookups, blending by randomly generated mixing bijections. We use techniques from [10, 12] to obtain the obfuscated implementation.
Specially, if we have bijections a:V {1,2,...,p} or :E {1,2,...,q} then the labelings are called respectively a vertex labeling or a edge labeling.
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. The cardinality [[absolute value of X].sub.f] of a weighted set (X, f) is given by