bijective
Adjective

bijective (not comparable)

  1. (mathematics, of a map) Both injective and surjective.
    • 1987, James S. Royer, A Connotational Theory of Program Structure, Springer, Lecture Notes in Computer Science 273, page 15 ↗,
      Then, by a straightforward, computable, bijective numerical coding, this idealized FORTRAN determines an EN.[effective numbering] (Note: In this FORTRAN example, we could have omitted restrictions on I/O and instead used a computable, bijective, numerical coding for inputs and outputs to get another EN determined by FORTRAN.)
    • 1993, Susan Montgomery, Hopf Algebras and Their Actions on Rings, American Mathematical Society, Conference Board of the Mathematical Sciences, Regional Conference Series in Mathematics, Number 83, page 124 ↗,
      Recent experience indicates that for infinite-dimensional Hopf algebras, the “right” definition of Galois is to require that \beta be bijective.
    • 2008, B. Aslan, M. T. Sakalli, E. Bulus, Classifying 8-Bit to 8-Bit S-Boxes Based on Power Mappings, Joachim von zur Gathen, José Luis Imana, Çetin Kaya Koç (editors), Arithmetic of Finite Fields: 2nd International Workshop, Springer, Lecture Notes in Computer Science 5130, page 131 ↗,
      Generally, there is a parallel relation between the maximum differential value and maximum LAT value for bijective S-boxes.
    • 2010, Kang Feng, Mengzhao Qin, Symplectic Geometric Algorithms for Hamiltonian Systems, Springer, page 39 ↗,
      An isomorphism is a bijective homomorphism.
    • 2012 [Introduction to Graph Theory, McGraw-Hill], Gary Chartrand, Ping Zhang, A First Course in Graph Theory, 2013, Dover, Revised and corrected republication, page 64 ↗,
      The proof that isomorphism is an equivalence relation relies on three fundamental properties of bijective functions (functions that are one-to-one and onto): (1) every identity function is bijective, (2) the inverse of every bijective function is also bijective, (3) the composition of two bijective functions is bijective.
  2. (mathematics) Having a component that is (specified to be) a bijective map; that specifies a bijective map.
    • 2002, Proceedings of the 34th Annual ACM Symposium on the Theory of Computing, Association for Computing Machinery, page 774 ↗,
      Proving the conjecture is equivalent to constructing a PCP that reads 2 symbols and accepts iff these symbols satisfy a bijective constraint.
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