A Survey of Cameron-Liebler Sets and Low Degree Boolean Functions in Grassmann Graphs
Ferdinand Ihringer
TL;DR
This survey reviews Cameron-Liebler sets and low degree Boolean functions across various graph types, highlighting their roles in finite geometry, coding, and cryptography within the framework of association schemes.
Contribution
It compiles and discusses key results on Cameron-Liebler sets and Boolean functions in Grassmann and related graphs, emphasizing their interdisciplinary applications.
Findings
Cameron-Liebler sets are characterized in Grassmann graphs
Low degree Boolean functions relate to combinatorial designs
Connections to coding theory and cryptography are explored
Abstract
We survey results for Cameron-Liebler sets and low degree Boolean functions for Hamming graphs, Johnson graphs and Grassmann graphs from the point of view of association schemes. This survey covers selected results in finite geometry, Boolean function analysis, design theory, coding theory, and cryptography.
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Taxonomy
TopicsGraph theory and applications · Graph Labeling and Dimension Problems · Topological and Geometric Data Analysis