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- W2005683145 abstract "A well-known theorem of Knuth establishes a bijection between permutations in S ( N ) with no decreasing subsequence of length three and rectangular standard Young tableaux of shape R ( 2 , N ) . We prove an asymptotic version of this result: for any fixed integer d ⩾ 2 , the number of permutations in S ( d n ) with no decreasing subsequence of length d + 1 is asymptotically equal, as n → ∞ , to the number of standard Young tableaux on the rectangle R ( d , 2 n ) . This yields a new proof of Regevʼs theorem on the asymptotic number of permutations without long decreasing subsequences, and consequently an alternative, elementary evaluation of Mehtaʼs integral at β = 2 ." @default.
- W2005683145 created "2016-06-24" @default.
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- W2005683145 date "2011-07-01" @default.
- W2005683145 modified "2023-09-29" @default.
- W2005683145 title "An asymptotic version of a theorem of Knuth" @default.
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- W2005683145 doi "https://doi.org/10.1016/j.aam.2010.04.001" @default.
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