Group inequalities
The Ingleton inequality is a significant concept in both information theory and matroid theory, providing a crucial link between event probabilities and the im- portance of sets within matroids. This final year thesis explores the application of group theory to investigate the validity of this in...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Final Year Project |
| Language: | English |
| Published: |
Nanyang Technological University
2024
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/175578 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | The Ingleton inequality is a significant concept in both information theory and
matroid theory, providing a crucial link between event probabilities and the im-
portance of sets within matroids. This final year thesis explores the application of
group theory to investigate the validity of this inequality in previously unexplored
scenarios. Beginning with an examination of the symmetric group S5, known to
violate the inequality, we break down the known proof for abelian groups to in-
vestigate the reasons. We then extend our study to include the family of dihedral
groups, by examining the structure of dihedral groups, and its implication on the
Ingleton inequality. Our investigation concludes with the application of Goursat’s
Lemma to analyze how the inequality behaves on the direct product of abelian
and non-abelian groups. Through these methodologies, the aim is to deepen the
understanding of the Ingleton inequality and uncover potential insights with impli-
cations for both theoretical and practical domains within information and matroid
theory. |
|---|