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- W2797472282 abstract "An ordered set partition of ${1,2,ldots,n}$ is a partition with an ordering on the parts. Let $mathcal{OP}_{n,k}$ be the set of ordered set partitions of $[n]$ with $k$ blocks. Godbole, Goyt, Herdan and Pudwell defined $mathcal{OP}_{n,k}(sigma)$ to be the set of ordered set partitions in $mathcal{OP}_{n,k}$ avoiding a permutation pattern $sigma$ and obtained the formula for $|mathcal{OP}_{n,k}(sigma)|$ when the pattern $sigma$ is of length $2$. Later, Chen, Dai and Zhou found a formula algebraically for $|mathcal{OP}_{n,k}(sigma)|$ when the pattern $sigma$ is of length $3$. In this paper, we define a new pattern avoidance for the set $mathcal{OP}_{n,k}$, called $mathcal{WOP}_{n,k}(sigma)$, which includes the questions proposed by Godbole, Goyt, Herdan and Pudwell. We obtain formulas for $|mathcal{WOP}_{n,k}(sigma)|$ combinatorially for any $sigma$ of length $ 3$. We also define 3 kinds of descent statistics on ordered set partitions and study the distribution of the descent statistics on $mathcal{WOP}_{n,k}(sigma)$ for $sigma$ of length $3$." @default.
- W2797472282 created "2018-04-24" @default.
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- W2797472282 date "2018-04-19" @default.
- W2797472282 modified "2023-09-24" @default.
- W2797472282 title "Patterns in words of ordered set partitions" @default.
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- W2797472282 doi "https://doi.org/10.48550/arxiv.1804.07087" @default.
- W2797472282 hasPublicationYear "2018" @default.
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