On group violations of inequalities in five subgroups
| Autor: | Nadya Markin, Frederique Oggier, Eldho K. Thomas |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
FOS: Computer and information sciences
Algebra and Number Theory Rank (linear algebra) Computer Networks and Communications Group (mathematics) Computer Science - Information Theory Information Theory (cs.IT) Applied Mathematics 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology Lattice of subgroups 01 natural sciences Linear subspace Combinatorics Linear inequality 010201 computation theory & mathematics Symmetric group 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Order (group theory) Random variable Mathematics |
| Zdroj: | Advances in Mathematics of Communications. 10:871-893 |
| ISSN: | 1930-5346 |
| DOI: | 10.3934/amc.2016047 |
| Popis: | In this paper we use group theoretic tools to obtain random variables which violate linear rank inequalities, that is inequalities which always hold on ranks of subspaces. We consider ten of the 24 (non-Shannon type) generators of linear rank inequalities in five variables and look at them as group inequalities. We prove that for primes $p,q$, groups of order $pq$ always satisfy these ten group inequalities. We give partial results for groups of order $p^2q$, and find that the symmetric group $S_4$ is the smallest group to yield violations for two among the ten group inequalities. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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