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 |
id |
sg-ntu-dr.10356-175578 |
---|---|
record_format |
dspace |
spelling |
sg-ntu-dr.10356-1755782024-05-06T15:37:20Z Group inequalities Eng, Jasper Min Lun Frederique Elise Oggier School of Physical and Mathematical Sciences Frederique@ntu.edu.sg Mathematical Sciences Math 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. Bachelor's degree 2024-04-30T05:30:30Z 2024-04-30T05:30:30Z 2024 Final Year Project (FYP) Eng, J. M. L. (2024). Group inequalities. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/175578 https://hdl.handle.net/10356/175578 en application/pdf Nanyang Technological University |
institution |
Nanyang Technological University |
building |
NTU Library |
continent |
Asia |
country |
Singapore Singapore |
content_provider |
NTU Library |
collection |
DR-NTU |
language |
English |
topic |
Mathematical Sciences Math |
spellingShingle |
Mathematical Sciences Math Eng, Jasper Min Lun Group inequalities |
description |
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. |
author2 |
Frederique Elise Oggier |
author_facet |
Frederique Elise Oggier Eng, Jasper Min Lun |
format |
Final Year Project |
author |
Eng, Jasper Min Lun |
author_sort |
Eng, Jasper Min Lun |
title |
Group inequalities |
title_short |
Group inequalities |
title_full |
Group inequalities |
title_fullStr |
Group inequalities |
title_full_unstemmed |
Group inequalities |
title_sort |
group inequalities |
publisher |
Nanyang Technological University |
publishDate |
2024 |
url |
https://hdl.handle.net/10356/175578 |
_version_ |
1806059802158170112 |