3 problems

Rational shuffle generating-function conjecture. The polynomial

Let ${\mathcal{PW}}_m^n$ denote the set of $(m,n)$-parking words, and let ${\mathsf{area}}$ and ${\mathsf{dinv}}$ be the associated statistics. Gorsky, Mazin, and Vazirani defined…

Pak–Stanley bijectivity conjecture. The map $\mathcal{PS}_m$ is a bijection from $\operatorname{Stab}(n,m)$ to the set of $(n,m)$-parking functions for all $m$.