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

M. Ibrahim *

Department of Mathematics, Usmanu Danfodiyo University, Sokoto State, Nigeria.

S. H. Isah

Department of Mathematics, Nasarawa State University Keffi, Nasarawa State, Nigeria.

*Author to whom correspondence should be addressed.


In this paper, we investigated anti-excedance statistics in \(\Gamma\)1-non deranged permutations, the permutation which fixes the first element in the permutations. This was accomplished by employing prime integers p \(\ge\) 5 in various calculations using this approach. The anti-excedance on \(\Gamma\)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 \(\omega\)\(\mathit{i}\)-1 \(\in\)Gp\(\Gamma\)1 is equal to the excedance tops sum of \(\omega\)\(\mathit{i}\) \(\in\)Gp\(\Gamma\)1 . Similarly, we observed those anti-excedance bottoms sum for any  \(\omega\)\(\mathit{i}\)-1 \(\in\)Gp\(\Gamma\)1 is equal to the excedance bottoms sum of  \(\omega\)\(\mathit{i}\) \(\in\)Gp\(\Gamma\)1 other properties were also observed.

Keywords: Anti-excedance, \(\Gamma\)1-non deranged permutations, anti-excedance tops sum, anti-excedance bottoms sum, anti-excedance difference

How to Cite

Ibrahim , M., & Isah , S. H. (2023). Connections between Anti-Excedance and Excedance on the \(\Gamma\)1-non Deranged Permutations. Asian Research Journal of Mathematics, 19(10), 114–123.


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