Let $P$ the set of all permutations $(x_1, \ldots, x_n)$ of numbers $(1, \ldots,10)$ and $L$ the subset of $P$ where $\sum_{j=1}^{n}jx_j> a$. To use Hasting-Metropolis algorithm I followed the following steps to read a book on te subject.
Define the q transition probability function as follows. $$q(s,t) = \frac{1}{|N(s)|}, \text{if $t \in N(s)$}$$ With $N(s)$ defined as the set of neighbors of $s$, and $|N(s)|$ equal to the number of elements in the set $N(s)$, and so $$ \alpha(s,t) = min(|N(s)|/|N(t)|, 1)$$
My main doubt is what "neighbor" in this context. Because any permutation will have the same number of neighbors then $\alpha$ will always give 1