Symmetric sequencings and other combinatorial properties of large groups

TL;DR

This paper proves conjectures related to symmetric and 2-sequencings in large groups, extending the understanding of combinatorial properties and sequence extensions in both abelian and non-abelian groups.

Contribution

It establishes the validity of Anderson's and Bailey's conjectures for large groups and explores extensions of various sequencing concepts in different group contexts.

Findings

Proves Anderson's conjecture for large groups

Proves Bailey's conjecture for large groups

Provides new results on double sequencings in abelian and non-abelian groups

Abstract

We prove that Anderson's conjecture on symmetric sequencings and Bailey's conjecture on 2-sequencings hold for sufficiently large groups. In addition, we discuss extensions of partial harmonious sequences and partial R-sequencings. Several further results on double sequencings are presented, both in the context of abelian groups and for sufficiently large non-abelian groups.