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Cyclic permutations avoiding patterns in both one-line and cycle forms (2312.05145v2)
Published 8 Dec 2023 in math.CO
Abstract: Let $\sigma$ and $\tau$ be patterns of length three; that is $\sigma, \tau \in {123,132,213,231,312,321}$. In this paper, we enumerate the set of cyclic permutations in $\mathcal{S}_n$ that avoid $\sigma$ in their one-line notation and another pattern $\tau$ in their cycle notation.
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