6 problems

Dijoin additivity conjecture. The equality

Let merge sort operate on $n=2^m$ items, let each comparison be erroneous with probability $p=\lambda/n$, and let the number of inversions in its output be normalized in the same w…

Unimodality conjecture. For any consecutive permutation pattern $\pi$, if $n\geqslant |\pi|+2$, then the sequence

The threshold interpolation conjecture. If $n^{1-1/s}\ll m$ and $\binom{n}{2}-m\gg n^{1-1/s'}$, then

For a classical pattern $p$, let $a_{n,k}(p)$ be the number of length-$n$ permutations avoiding $p$ and having exactly $k$ inversions. The non-increasing-pattern monotonicity conje…

For integers $n$ and $k$, let $a_{n,k}$ be the number of permutations of length $n$ that avoid $1324$ and have exactly $k$ inversions, where an inversion is a pair $(i,j)$ with…