5 problems

LSB Euler–Mahonian conjecture. The statistics \mathop{\text{\text{\rm cmaj}\text{LSB}}} and \mathop{\text{\text{\rm cinv}\text{LSB}}} are Euler–Mahonian on ordered partitio…

Euler–Mahonian pairing conjecture. Each of the eight statistics

Let ${\cal OP}_n^k$ be the set of ordered $k$-partitions of $[n]$, and let $\mathop{\rm bmaj}$ and $\mathop{\rm binv}$ be the block-major index and block-inversion statistics. Let…

Let $\mathrm{FR}_n$ denote the set of Fubini rankings on $n$ competitors, and let $\mathrm{flat\_runs}_k(\mathrm{FR}_n)$ denote the flattened Fubini rankings with $k$ runs of ascen…

An ordered partition of $[2k]$ with $k$ blocks of size $2$ is counted by $op_{[2^k]}(123)$ when it avoids the permutation pattern $123$. Godbole–Goyt–Herdan–Pudwell's recurrence co…