Honors Project On-Campus Access Only
We study a subfamily Ln 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 Ln are enumerated by the Fibonacci numbers. We then examine those maximum elements of Ln 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.
Robertson, Paige, "Enumerating Maximal Binary Triangles" (2022). Mathematics, Statistics, and Computer Science Honors Projects. 68.
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