Conjecture on Supersequence Lower Bound related to Connell Sequence

TL;DR

This paper establishes a new lower bound of 52 for supersequences over eight elements, disproving a previous conjecture and offering insights into the internal structure of such sequences.

Contribution

It provides the first proof of the minimum supersequence size for eight elements and challenges the conjectured lower bound based on the Connell sequence.

Findings

Minimum supersequence size over eight elements is 52

Disproves the conjecture relating to Connell sequence lower bound

Provides structural insights into supersequence segments

Abstract

This paper proves the minimum size of a supersequence over a set of eight elements is 52. This disproves a conjecture that the lower bound of the supersequence is the partial sum of the geometric Connell sequence. By studying the internal distribution of individual elements within sub-strings of the supersequence called segments, the proof provides important results on the internal structure that could help to understand the general lower bound problem for finite sets.