RESTRICTED BIJECTIONS ON THE GAMMA_1 NON DERANGED PERMUTATION GROUP |Asian Journal of Mathematics

The study of the combinatorial properties of permutations relies heavily on Euler-Mahonian statistics. On the l.JPG-non deranged permutations, we construct the Euler-Mahonian statistics in this paper. We 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 by redefining various Euler-Mahonian statistics with regard to the l.JPG-non deranged permutations. We also observe that the height of the weighted Motzkin route of I is the same as the height of the weighted Motzkin path of w.JPG when the bijections (, Francon and Viennot FV' and Foata and Zilberger FZ) are restricted to the l1.JPG -non deranged permutation group g.JPG.

Please see the link :- https://www.ikprress.org/index.php/AJOMCOR/article/view/4200