RESTRICTED BIJECTIONS ON THE GAMMA_1 NON DERANGED PERMUTATION GROUP
KAZEEM OLALEKAN AREMU *
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
ABOR ISA GARBA *
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
MANIRU IBRAHIM
*
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
STEPHEN BUORO
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
*Author to whom correspondence should be addressed.
Abstract
Euler-Mahonian statistics are of great importance in studying the combinatorial properties of permutations. In this work we compute the Euler-Mahonian statistics on the 
-non deranged permutations. We redefine some of the Euler-Mahonian statistics with respect to the -non deranged permutations and show that the Right Embracing Number of -non deranged permutation 
is equidistributed with the Left Embracing Number 
and that the 
is equidistributed with the 
. Furthermore, we restrict the bijections (Φ, Francon and Viennot ΨFV' and Foata and Zilberger ΨFZ) on the 
-non deranged permutation group 
and observe that the height of the weighted Motzkin path of ωi is the same as the height of weighted Motzkin path of 
Keywords: Permutation, Bijection, Permutation Statistic, Motzkin Path