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- W4300806472 abstract "Linked partitions are introduced by Dykema in the study of transforms in free probability theory, whereas permutation tableaux are introduced by Steingr'{i}msson and Williams in the study of totally positive Grassmannian cells. Let $[n]={1,2,ldots,n}$. Let $L(n,k)$ denote the set of linked partitions of $[n]$ with $k$ blocks, let $P(n,k)$ denote the set of permutations of $[n]$ with $k$ descents, and let $T(n,k)$ denote the set of permutation tableaux of length $n$ with $k$ rows. Steingr'{i}msson and Williams found a bijection between the set of permutation tableaux of length $n$ with $k$ rows and the set of permutations of $[n]$ with $k$ weak excedances. Corteel and Nadeau gave a bijection from the set of permutation tableaux of length $n$ with $k$ columns to the set of permutations of $[n]$ with $k$ descents. In this paper, we establish a bijection between $L(n,k)$ and $P(n,k-1)$ and a bijection between $L(n,k)$ and $T(n,k)$. Restricting the latter bijection to noncrossing linked partitions, we find that the corresponding permutation tableaux can be characterized by pattern avoidance." @default.
- W4300806472 created "2022-10-04" @default.
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- W4300806472 date "2013-05-23" @default.
- W4300806472 modified "2023-09-23" @default.
- W4300806472 title "Linked Partitions and Permutation Tableaux" @default.
- W4300806472 doi "https://doi.org/10.48550/arxiv.1305.5357" @default.
- W4300806472 hasPublicationYear "2013" @default.
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