On Hyperoctahedral Enumeration System, Application to Signed Permutations
Iharantsoa Vero Raharinirina *
Department of Mathematics and Computer Science, Faculty of Sciences, University of Antananarivo, BP 906 Antananarivo 101, Madagascar.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we give the definition and basic facts about hyperoctahedral number system. There is a natural correspondence between the integers expressed in the latter and the elements of the hyperoctahedral group when we use the inversion statistic on this group to code the signed permutations. We show that this correspondence provides a way with which the signed permutations group can be ordered. With this classication scheme, we can find the r-th signed permutation from a given number r and vice versa without consulting the list in lexicographical order of the elements of the signed permutations group.
Keywords: Hyperoctahedral enumeration system, signed permutation code, inversion statistic, lexico- graphic order.