Given a set of naturals [n]:{1,2,3,...,n}, we repeatably select m elements from [n] to make a sorted set ${x_1,x_2,...,x_n}$ satisfying $x_i \notless x_j$ for i>=j.

What the probability $p(i<=k)$ where i satisfies (1) $x_i-x_{i+1}>=L$ and (2) $x_j-x_{j+1} < L$ for j<i.

Usually, $m << n$, $k << n$, and L~n/m.

Given a set of naturals [n]:{1,2,3,...,n}, we repeatably select m elements from [n] to make a sorted set ${x_1,x_2,...,x_m}$ satisfying $x_i >= x_j$ for i>=j.

What the probability $p(i<=k)$ where i satisfies (1) $x_i-x_{i+1}>=L$ and (2) $x_j-x_{j+1} < L$ for $j < i$.

Usually, $m << n$, $k << n$, and L~n/m.

Given a set of naturals [n]:{1,2,3,...,n}, we repeatably select m elements from [n] to make a sorted set ${x_1,x_2,...,x_n}$ satisfying $x_i>=x_j$ for i>=j.

What the probability $p(i<=k)$ where i satisfies $x_i-x_{i+1}>=L$ and $x_j-x_{j-1}<L$ for j<=i.

Usually, m<<n, k<<n, and L~n/m.

Given a set of naturals [n]:{1,2,3,...,n}, we repeatably select m elements from [n] to make a sorted set ${x_1,x_2,...,x_n}$ satisfying $x_i \notless x_j$ for i>=j.

What the probability $p(i<=k)$ where i satisfies (1) $x_i-x_{i+1}>=L$ and (2) $x_j-x_{j+1} < L$ for j<i.

Usually, $m << n$, $k << n$, and L~n/m.