RESTRICTED BIJECTIONS ON THE GAMMA_1 NON DERANGED PERMUTATION GROUP

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