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- W3204430434 abstract "A permutation is $k$-coverable if it can be partitioned into $k$ monotone subsequences. Barber conjectured that, for any given permutation, if every subsequence of length ${k+2 choose 2}$ is $k$-coverable then the permutation itself is $k$-coverable. This conjecture, if true, would be best possible.
 Our aim in this paper is to disprove this conjecture for all $k geqslant 3$. In fact, we show that for any $k$ there are permutations such that every subsequence of length at most $(k/6)^{2.46}$ is $k$-coverable while the permutation itself is not." @default.
- W3204430434 created "2021-10-11" @default.
- W3204430434 creator A5010571556 @default.
- W3204430434 date "2021-09-24" @default.
- W3204430434 modified "2023-09-27" @default.
- W3204430434 title "Partitioning Permutations into Monotone Subsequences" @default.
- W3204430434 doi "https://doi.org/10.37236/10267" @default.
- W3204430434 hasPublicationYear "2021" @default.
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