Open AccessEnumeration and coding methods for a class of permutations and reversible logical gates
Author(s) -
C. Karanikas,
Nikolaos Atreas
Publication year - 2018
Publication title -
facta universitatis. series electronics and energetics/facta universitatis. series: electronics and energetics
Language(s) - English
Resource type - Journals
eISSN - 2217-5997
pISSN - 0353-3670
DOI - 10.2298/fuee1802241k
Subject(s) - enumeration , shuffling , permutation (music) , binary number , coding (social sciences) , logical matrix , mathematics , set (abstract data type) , invertible matrix , class (philosophy) , algorithm , theoretical computer science , computer science , combinatorics , discrete mathematics , arithmetic , group (periodic table) , statistics , physics , chemistry , organic chemistry , artificial intelligence , acoustics , pure mathematics , programming language
We introduce a great variety of coding methods for Boolean sparse invertible matrices and we use these methods to create a variety of bijections on the permutation group P(m) of the set {1,2,...,m}. Also, we propose methods for coding, enumerating and shuffling the set{0,...,2m?1}, i.e. the set of all m-bit binary arrays. Moreover we show that several well known reversible logic gates/circuits (on m-bit binary arrays) can be coded by sparse matrices.