What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?
- The numbers in each group are arranged in decreasing order.
- All the numbers of a subsequent group are greater than all the numbers of a preceding group.
- The first group consists of y elements: , which is possible by the condition .
- We divide the remaining elements into groups as follows. Let and . Note that and . The first r groups represent decreasing subsequences of the length :….The last groups represent decreasing subsequences of length p. (If , then all decreasing subsequences have the length p):,…
Conflicts of Interest
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Itskovich, E.J.; Levit, V.E. What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other? Algorithms 2019, 12, 237. https://doi.org/10.3390/a12110237
Itskovich EJ, Levit VE. What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other? Algorithms. 2019; 12(11):237. https://doi.org/10.3390/a12110237Chicago/Turabian Style
Itskovich, Elizabeth J., and Vadim E. Levit. 2019. "What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?" Algorithms 12, no. 11: 237. https://doi.org/10.3390/a12110237