Connections between Anti-Excedance and Excedance on the \(\Gamma\)1-non Deranged Permutations

In this paper, we investigated anti-excedance statistics in
1-non deranged permutations, the permutation which fixes the first element in the permutations. This was accomplished by employing prime integers p
5 in various calculations using this approach. The anti-excedance on
1- non deranged permutations is redefined in this study. The recursive formula for the anti-excedance number and excedance number is generated, we also show that anti-excedance tops sum for any
-1
Gp
1 is equal to the excedance tops sum of

Gp
1 . Similarly, we observed those anti-excedance bottoms sum for any
-1
Gp
1 is equal to the excedance bottoms sum of

Gp
1 other properties were also observed.