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...
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| Main Authors: | , |
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| Other Authors: | |
| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2012
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/94135 http://hdl.handle.net/10220/8769 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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