Elizabeth J. Itskovich, Vadim E. Levit
Abstract
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As a kind of converse of the celebrated Erd˝os-Szekeres theorem, we present a necessary and sufficient condition for a sequence of length n to contain a longest increasing subsequence and a longest decreasing subsequence of given lengths x and y, respectively.
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As a kind of converse of the celebrated Erd˝os-Szekeres theorem, we present a necessary and sufficient condition for a sequence of length n to contain a longest increasing subsequence and a longest decreasing subsequence of given lengths x and y, respectively.
Key concepts: Subsequence, Longest increasing subsequence, Converse, Longest common subsequence problem, Combinatorics, Sequence (biology), Mathematics, Biology