Honors Project - Open Access
We study the family An of sequences (a1, a2, ..., an) where 0 ≤ ak ≤ 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 An, including sequences whose largest entry is k and sequences missing the value k.
Simmons, Andrea L., "Staircase Arrangements of Pillars with Distinct Heights" (2023). Mathematics, Statistics, and Computer Science Honors Projects. 81.
© Copyright is owned by author of this document