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- W3210088247 abstract "We continue our study of a new boundedness condition for affine permutations, motivated by the fruitful concept of periodic boundary conditions in statistical physics. We focus on bounded affine permutations of size $N$ that avoid the monotone decreasing pattern of fixed size $m$. We prove that the number of such permutations is asymptotically equal to $(m-1)^{2N} N^{(m-2)/2}$ times an explicit constant as $Ntoinfty$. For instance, the number of bounded affine permutations of size $N$ that avoid $321$ is asymptotically equal to $4^N (N/4pi)^{1/2}$. We also prove a permuton-like result for the scaling limit of random permutations from this class, showing that the plot of a typical bounded affine permutation avoiding $mcdots1$ looks like $m-1$ random lines of slope $1$ whose $y$ intercepts sum to $0$." @default.
- W3210088247 created "2021-11-08" @default.
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- W3210088247 date "2021-10-21" @default.
- W3210088247 modified "2023-10-18" @default.
- W3210088247 title "Bounded Affine Permutations II. Avoidance of Decreasing Patterns" @default.
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- W3210088247 doi "https://doi.org/10.1007/s00026-021-00553-4" @default.
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