Counting the number of permutations with longest increasing subsequence of a certain length

Zhiming Feng Tsinghua University High School

S.-T. Yau High School Science Awarded Papers mathscidoc:1702.35007

2016
This essay mainly involves a method to count the number of permutations of size n with length of the longest increasing subsequence equal to 2. The question is raised as the research project of Algebraic Combinatorics in 2016 Tsinghua Math Camp. This essay will show the relationshi between a permutation's longest increasing subsequence andits correspondingRobinson-Schensted map. Moreover, theessay will develop a general formula to count thenumberwith the help of the hook length formula.
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@inproceedings{zhiming2016counting,
  title={Counting the number of permutations with longest increasing subsequence of a certain length},
  author={Zhiming Feng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170227152411357390526},
  year={2016},
}
Zhiming Feng. Counting the number of permutations with longest increasing subsequence of a certain length. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170227152411357390526.
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