Random Permutation

**Sampras** · January 31st 2011, 02:40 PM

Suppose $\pi$ is a random permutation of $\mathbb{Z}_n$ . How would you determine the probability that $\pi(i+1)-\pi(i) \pmod n < n/2$ ? We know that $\pi(i+1)-\pi(i)$ is maximum at $n-1$ in $\mathbb{Z}_n$ .

**Sampras** · February 1st 2011, 04:51 PM

Perhaps we could use Inclusion-Exclusion? In other words, find the probability that $\pi(i+1)-\pi(i) > n/2$ (i.e. the $i$ th and $i+1$ -st places differ by more than $n/2$ ?

Thread: Random Permutation

LinkBack

Thread Tools

Display

Random Permutation

Similar Math Help Forum Discussions

Probability and random random varible question

exponential random variable with a random mean?

Finding the marginal distribution of a random variable w/ a random variable parameter

What's the difference between discrete random variables and continous random variable

Random vectors & random matrices (1)

Search Tags