Sorting probability for large Young diagrams

Abstract

Sorting probability for large Young diagrams, Discrete Analysis 2021:24, 57 pp. Let $P=(X,\leq_P)$ be a finite partially ordered set (or _poset_, for short). A _linear extension_ $L$ of $P$ is a total ordering $\leq_L$ on $X$ such that for every $x,y\in X$, if $x\leq_Py$, then $x\leq_Ly$. It is an easy exercise to prove that every poset has a linear extension: indeed, if any two elements $x,y$ are incomparable in $P$, then one can choose to add to $P$ the inequality $x