Staircase Arrangements of Pillars with Distinct Heights

Authors

Andrea L. SimmonsFollow

Document Type

Honors Project - Open Access

Abstract

We study the family A_n of sequences (a₁, a₂, ..., a_n) where 0 ≤ a_k ≤ k and nonzero entries are distinct. We show that these sequences are in bijection with the set partitions of [n + 1]. These sequences have a natural poset structure, and we analyze the maximal chains within this poset. Finally, we explore various subfamilies of A_n, including sequences whose largest entry is k and sequences missing the value k.

Recommended Citation

Simmons, Andrea L., "Staircase Arrangements of Pillars with Distinct Heights" (2023). Mathematics, Statistics, and Computer Science Honors Projects. 81.
https://digitalcommons.macalester.edu/mathcs_honors/81