Enumerating Maximal Binary Triangles

Authors

Paige RobertsonFollow

Document Type

Honors Project On-Campus Access Only

Abstract

We study a subfamily L_n of binary triangles with weakly increasing columns and the preexisting partial ordering it inherits from the larger binary triangle family. Through the study of this subfamily’s structure we show that the maximal elements of L_n are enumerated by the Fibonacci numbers. We then examine those maximum elements of L_n which also have maximum total sum and show that this subset is enumerated by OEIS sequence A209561 and the corresponding sums are given by OEIS sequence A023536. We conclude with two methods of constructing these maximal elements with maximum sums, one recursive and one explicit.

Recommended Citation

Robertson, Paige, "Enumerating Maximal Binary Triangles" (2022). Mathematics, Statistics, and Computer Science Honors Projects. 68.
https://digitalcommons.macalester.edu/mathcs_honors/68