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arXiv · 1907.03881

Kostka Numbers and Longest Increasing Subsequences

Arjun Krishnan·Scott Neville
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Abstract

A classical bijection relates certain Kostka numbers, the Catalan numbers, and permutations of length $n$ with longest increasing subsequence (LIS) of length at most $2.$ We generalize this bijection and find Kostka numbers which count the number of permutations of $n$ with LIS length at most $w,$ the number of permutations with $(1, \cdots, w)$ as a LIS, and other similar subsets of permutations.

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Arjun Krishnan, Scott Neville. 2020-07-21. Kostka Numbers and Longest Increasing Subsequences. https://arxiv.org/abs/1907.03881

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