Period mimicry: A note on the $(-1)$-evaluation of the peak polynomials

TL;DR

This paper investigates a sequence related to peak polynomials, revealing an initial periodic pattern that transitions into complex non-periodic fluctuations, highlighting intriguing behaviors in mathematical sequences.

Contribution

It introduces and analyzes a sequence associated with peak polynomials, uncovering a novel phenomenon of initial periodicity followed by non-periodic fluctuations.

Findings

Sequence shows initial periodic behavior.

Sequence exhibits non-periodic fluctuations later.

Highlights complex dynamics in polynomial-related sequences.

Abstract

We briefly explore a sequence that came up in recent work of Tirrell and Zhuang. We discover an unusual phenomenon where the sequence appears at first to have periodic behavior but eventually has non-periodic fluctuations.