6 problems

For each $n\geq 1$, let $P_n(x)=\sum_k P_{n,k}x^k$, where $P_{n,k}$ is the number of permutations of $[n]=\{1,2,\ldots,n\}$ whose longest increasing subsequence has length $k$. A p…

Non-central moment conjecture. For all $r\ge 1$, if $n$ is sufficiently large in terms of $m$, then

Central moment conjecture. For all $r\ge 1$, if $n$ is sufficiently large in terms of $m$, then

Diaconis–Graham–He–Spiro conjecture. This upper bound for $\mathbb{E}[L^1_{m,n}(\pi)]$ is asymptotically tight when $n$ is sufficiently large in terms of $m$.

For each $n\geq 1$, let $P_n(x)=\sum_k P_{n,k}x^k$, where $P_{n,k}$ is the number of permutations of $[n]=\{1,2,\ldots,n\}$ whose longest increasing subsequence has length $k$. A p…

For each $n\geq 1$, let $P_n(x)=\sum_k P_{n,k}x^k$, where $P_{n,k}$ is the number of permutations of $[n]=\{1,2,\ldots,n\}$ whose longest increasing subsequence has length $k$. A p…