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- W3025785615 abstract "Sch{u}tzenberger's promotion operator is an extensively-studied bijection that permutes the linear extensions of a finite poset. We introduce a natural extension $partial$ of this operator that acts on all labelings of a poset. We prove several properties of $partial$; in particular, we show that for every labeling $L$ of an $n$-element poset $P$, the labeling $partial^{n-1}(L)$ is a linear extension of $P$. Thus, we can view the dynamical system defined by $partial$ as a sorting procedure that sorts labelings into linear extensions. For all $0leq kleq n-1$, we characterize the $n$-element posets $P$ that admit labelings that require at least $n-k-1$ iterations of $partial$ in order to become linear extensions. The case in which $k=0$ concerns labelings that require the maximum possible number of iterations in order to be sorted; we call these labelings tangled. We explicitly enumerate tangled labelings for a large class of posets that we call inflated rooted forest posets. For an arbitrary finite poset, we show how to enumerate the sortable labelings, which are the labelings $L$ such that $partial(L)$ is a linear extension." @default.
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- W3025785615 date "2020-05-14" @default.
- W3025785615 modified "2023-09-27" @default.
- W3025785615 title "Promotion Sorting." @default.
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