Document Type
Honors Project - Open Access
Abstract
We study the poset structures for two families of pattern avoiding permutations. An n-permutation is a list of the numbers [n]={1,2,...,n}. A permutation is 321-avoiding when it does not contain a decreasing subsequence of length 3. A poset (partially ordered set) is a set such that some elements can be compared with one another. Using Lehmer codes, we define a poset for 321-avoiding permutations. We then fully describe the six lowest levels of this poset. We then consider the analogous poset for 123-avoiding permutations (which don't contain an increasing subsequence of length 3) and fully describe the three lowest levels.
Recommended Citation
Sinclair, Avery, "Level Sets for Lehmer Codes of Pattern Avoiding Permutations" (2026). Mathematics, Statistics, and Computer Science Honors Projects. 102.
https://digitalcommons.macalester.edu/mathcs_honors/102
© Copyright is owned by author of this document
