Maximal Symmetric Difference-Free Families of Subsets of $[n]$

TL;DR

This paper characterizes the structure of maximal symmetric difference-free families of subsets of [n], advancing understanding of combinatorial set families with specific difference constraints.

Contribution

It provides a complete characterization of maximal symmetric difference-free families, a new class of set families not previously fully understood.

Findings

Complete characterization of maximal symmetric difference-free families.

Identification of structural properties unique to these families.

Extension of combinatorial theory on set families with difference constraints.

Abstract

Union-free families of subsets of $[n]=\{1,... n\}$ have been studied in \cite{FF}. In this paper, we provide a complete characterization of maximal {\it symmetric difference}-free families of subsets of $[n]$.