Homomesy in products of two chains
Homomesy in products of two chains
Many invertible actions $\tau$ on a set ${\mathcal{S}}$ of combinatorial objects, along with a natural statistic $f$ on ${\mathcal{S}}$, exhibit the following property which we dub \textbf{homomesy}: the average of $f$ over each $\tau$-orbit in ${\mathcal{S}}$ is the same as the average of $f$ over the whole set ${\mathcal{S}}$. This …