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- W2983670020 abstract "Let $P_n^{text{sep}}$ denote the uniform probability measure on the set of separable permutations in $S_n$. Let $mathbb{N}^*=mathbb{N}cup{infty}$ with an appropriate metric and denote by $S(mathbb{N},mathbb{N}^*)$ the compact metric space consisting of functions $sigma={sigma_i}_{ i=1}^infty$ from $mathbb{N}$ to $mathbb{N}^*$ which are injections when restricted to $sigma^{-1}(mathbb{N})$rm; that is, if $sigma_i=sigma_j$, $ineq j$, then $sigma_i=infty$. Extending permutations $sigmain S_n$ by defining $sigma_j=j$, for $j>n$, we have $S_nsubset S(mathbb{N},mathbb{N}^*)$. We show that ${P_n^{text{sep}}}_{n=1}^infty$ converges weakly on $S(mathbb{N},mathbb{N}^*)$ to a limiting distribution of regenerative type, which we calculate explicitly." @default.
- W2983670020 created "2019-11-22" @default.
- W2983670020 creator A5032276033 @default.
- W2983670020 date "2019-11-13" @default.
- W2983670020 modified "2023-09-27" @default.
- W2983670020 title "The Infinite Limit of Separable Permutations" @default.
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