Discrete Mathematics and Combinatorics Commons^™

Long Increasing Subsequences, Hannah Friedman

HMC Senior Theses

In my thesis, I investigate long increasing subsequences of permutations from two angles. Motivated by studying interpretations of the longest increasing subsequence statistic across different representations of permutations, we investigate the relationship between reduced words for permutations and their RSK tableaux in Chapter 3. In Chapter 4, we use permutations with long increasing subsequences to construct a basis for the space of 𝑘-local functions.