A note on quasi-uniform distributions and Abelian group representability

• Main Authors: Thomas, Eldho K., Oggier, Frederique
• Other Authors: School of Physical and Mathematical Sciences
• Format: Conference or Workshop Item
• Language: English
• Published: 2012
• Subjects: DRNTU::Science::Mathematics
• Online Access: https://hdl.handle.net/10356/94135; http://hdl.handle.net/10220/8769
• Institution: Nanyang Technological University

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.