English

Kostka Numbers and Longest Increasing Subsequences

Combinatorics 2020-07-22 v2

Abstract

A classical bijection relates certain Kostka numbers, the Catalan numbers, and permutations of length nn with longest increasing subsequence (LIS) of length at most 2.2. We generalize this bijection and find Kostka numbers which count the number of permutations of nn with LIS length at most w,w, the number of permutations with (1,,w)(1, \cdots, w) as a LIS, and other similar subsets of permutations.

Keywords

Cite

@article{arxiv.1907.03881,
  title  = {Kostka Numbers and Longest Increasing Subsequences},
  author = {Arjun Krishnan and Scott Neville},
  journal= {arXiv preprint arXiv:1907.03881},
  year   = {2020}
}
R2 v1 2026-06-23T10:15:27.418Z