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- W2980348586 abstract "Abstract For $$tau in {S_3}$$ , let $$mu _n^tau $$ denote the uniformly random probability measure on the set of $$tau $$ -avoiding 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 $$sigma {rm{ = }}{ {sigma _i}} _{i = 1}^infty {rm{ }}$$ from $$mathbb {N}$$ to $${mathbb {N}^ * }$$ which are injections when restricted to $${sigma ^{ - 1}}(mathbb {N})$$ ; that is, if $${sigma _i}{rm{ = }}{sigma _j}$$ , $$i ne j$$ , then $${sigma _i} = infty $$ . Extending permutations $$sigma in {S_n}$$ by defining $${sigma _j} = j$$ , for $$j gt n$$ , we have $${S_n} subset S({mathbb{N}},{{mathbb{N}}^*})$$ . For each $$tau in {S_3}$$ , we study the limiting behaviour of the measures $${ mu _n^tau } _{n = 1}^infty $$ on $$S({mathbb{N}},{mathbb{N}^*})$$ . We obtain partial results for the permutation $$tau = 321$$ and complete results for the other five permutations $$tau in {S_3}$$ ." @default.
- W2980348586 created "2019-10-25" @default.
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- W2980348586 date "2019-10-14" @default.
- W2980348586 modified "2023-10-18" @default.
- W2980348586 title "The Infinite limit of random permutations avoiding patterns of length three" @default.
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- W2980348586 doi "https://doi.org/10.1017/s0963548319000270" @default.
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