RESTRICTED BIJECTIONS ON THE GAMMA_1 NON DERANGED PERMUTATION GROUP

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KAZEEM OLALEKAN AREMU
ABOR ISA GARBA
MANIRU IBRAHIM
https://orcid.org/0000-0002-9644-1921
STEPHEN BUORO

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 l.JPG-non deranged permutations. We redefine some of the Euler-Mahonian statistics with respect to the l.JPG-non deranged permutations and show that the Right Embracing Number of -non deranged permutation res.JPG is equidistributed with the Left Embracing Number les.JPG and that the res1.JPG is equidistributed with the res21.JPG. Furthermore, we restrict the bijections (Φ, Francon and Viennot ΨFV' and Foata and Zilberger ΨFZ) on the l1.JPG  -non deranged permutation group g.JPG and observe that the height of the weighted Motzkin path of ωi is the same as the height of weighted Motzkin path of w.JPG

Keywords:
Permutation, Bijection, Permutation Statistic, Motzkin Path

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How to Cite
AREMU, K., GARBA, A., IBRAHIM, M., & BUORO, S. (2019). RESTRICTED BIJECTIONS ON THE GAMMA_1 NON DERANGED PERMUTATION GROUP. Asian Journal of Mathematics and Computer Research, 25(8), 462-477. Retrieved from http://ikpress.org/index.php/AJOMCOR/article/view/4200
Section
Original Research Article