Monotone subsets in lattices and the Schensted shape of a Sós permutation

Karl Liechty, T. Kyle Petersen

For a fixed irrational number $\alpha$ and $n\in \mathbb{N}$, we look at the shape of the sequence $(f(1),\dots ,f(n))$ after Schensted insertion, where $f(i)=\alpha i\mathrm{mod}1$. Our primary…