Number Systems on Subgroups of Signed Permutation Groups
F. Patrick Rabarison, Hery Randriamaro · arXiv (Cornell University) · 2015
We aim to construct natural bijections, by means of the new introduced combinatorial statistic i-inversion, between the set of positive integers and subgroups of signed permutation groups. We first give the condition for two sequences of positive integers to be a number system. Number systems based on the cardinalities of subgroups of the signed permutation groups are constructed thereafter. Then we etablish one-to-one correspondences between the positive integers and the elements of these subgroups. Besides an example of application of these results on cryptography is given.