3 problems

Let ${\mathsf{A_n^k}}$ denote the set of $k$-arrangements of size $n$. For a $k$-arrangement represented by a permutation $\pi$, color each fixed point using a map from…

Let $[n]=\{1,2,\ldots,n\}$, let a 2-arrangement of $[n-1]$ be represented in permutation form, and let $\mathop{\sf des}\nolimits$ denote the number of descents. Descent-distributi…

Let ${\mathsf{A_n^k}}$ denote the set of $k$-arrangements of size $n$, represented in permutation and derangement forms, and let $\mathop{\sf des}\nolimits$ denote the descent stat…