A note on quasi-uniform distributions and Abelian group representability
In this note, we study quasi-uniform distributions that are obtained from finite groups. We derive a few simple properties of entropic vectors obtained from Abelian groups, and consider the problem of determining when non-Abelian groups can provide richer entropic vectors than Abelian groups. We foc...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Conference Paper |
| Language: | English |
| Published: |
2012
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/94135 http://hdl.handle.net/10220/8769 |
| _version_ | 1826118677387280384 |
|---|---|
| author | Thomas, Eldho K. Oggier, Frederique |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Thomas, Eldho K. Oggier, Frederique |
| author_sort | Thomas, Eldho K. |
| collection | NTU |
| description | In this note, we study quasi-uniform distributions that are obtained from finite groups. We derive a few simple properties of entropic vectors obtained from Abelian groups, and consider the problem of determining when non-Abelian groups can provide richer entropic vectors than Abelian groups. We focus in particular on the family of dihedral groups D2n, and show that when 2n is not a power of 2, the induced entropic vectors for two variables cannot be obtained from Abelian groups, contrarily to the case of D8 which does not provide more than Abelian groups. |
| first_indexed | 2024-10-01T04:47:23Z |
| format | Conference Paper |
| id | ntu-10356/94135 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:47:23Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | ntu-10356/941352023-02-28T19:17:29Z A note on quasi-uniform distributions and Abelian group representability Thomas, Eldho K. Oggier, Frederique School of Physical and Mathematical Sciences International Conference on Signal Processing and Communications (2012 : Bangalore, India) DRNTU::Science::Mathematics In this note, we study quasi-uniform distributions that are obtained from finite groups. We derive a few simple properties of entropic vectors obtained from Abelian groups, and consider the problem of determining when non-Abelian groups can provide richer entropic vectors than Abelian groups. We focus in particular on the family of dihedral groups D2n, and show that when 2n is not a power of 2, the induced entropic vectors for two variables cannot be obtained from Abelian groups, contrarily to the case of D8 which does not provide more than Abelian groups. Accepted version 2012-10-12T07:47:14Z 2019-12-06T18:51:18Z 2012-10-12T07:47:14Z 2019-12-06T18:51:18Z 2012 2012 Conference Paper Thomas, E. K., & Oggier, F. (2012). A note on quasi-uniform distributions and Abelian group representability. 2012 International Conference on Signal Processing and Communications (SPCOM), pp.1-5. https://hdl.handle.net/10356/94135 http://hdl.handle.net/10220/8769 10.1109/SPCOM.2012.6290020 164443 en © 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [DOI: http://dx.doi.org/10.1109/SPCOM.2012.6290020]. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics Thomas, Eldho K. Oggier, Frederique A note on quasi-uniform distributions and Abelian group representability |
| title | A note on quasi-uniform distributions and Abelian group representability |
| title_full | A note on quasi-uniform distributions and Abelian group representability |
| title_fullStr | A note on quasi-uniform distributions and Abelian group representability |
| title_full_unstemmed | A note on quasi-uniform distributions and Abelian group representability |
| title_short | A note on quasi-uniform distributions and Abelian group representability |
| title_sort | note on quasi uniform distributions and abelian group representability |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/94135 http://hdl.handle.net/10220/8769 |
| work_keys_str_mv | AT thomaseldhok anoteonquasiuniformdistributionsandabeliangrouprepresentability AT oggierfrederique anoteonquasiuniformdistributionsandabeliangrouprepresentability AT thomaseldhok noteonquasiuniformdistributionsandabeliangrouprepresentability AT oggierfrederique noteonquasiuniformdistributionsandabeliangrouprepresentability |