Asian Research Journal of Mathematics

Admissible Inversion on Γ1 Non-Deranged Permutations

M. S. Magami *

Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria.

M. Ibrahim

Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria.

*Author to whom correspondence should be addressed.

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Abstract

Some further theoretic properties of scheme called Γ₁ non deranged permutations, the permutation which fixes the first element in the permutations were identified and studied in relation to admissible inversion in this paper. This was done first through some computation on this scheme using prime number p ≥ 5, the admissible inversion descent aid (ω_p-1) is equi-distributed with descent number des (ω_p-1) and also showed that the admissible inversion set Ai (ω_i ) and admissible inversion set Ai (ω_p-i ) are disjoint.

Keywords: Inversion numbers, admissible inversion, descent number and Γ1-non deranged permutations.

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