2 problems

Let an $(n+1,n+1)$-combination be a subset of $[2n+2]$ of size $n+1$, encoded by a bitstring with $n+1$ ones. A star transposition is a step in which the element $1$ either enters…

For $n\geq 1$, let $N={2n+2\choose n+1}$, and let $\alpha$ be the flip sequence of a star transposition ordering of all $(n+1,n+1)$-combinations, with entries in $[2n+1]$. Write ……