English

The Entropy Region is not Closed Under Duality

Information Theory 2016-11-15 v1 math.IT

Abstract

We import a duality notion coming from polymatroids to define duality for information inequalities. We show that the entropy region for n5n\ge 5 is not closed under duality. Our result answers an open question of Mat\`u\v{s} (1992).

Cite

@article{arxiv.1611.04109,
  title  = {The Entropy Region is not Closed Under Duality},
  author = {Tarik Kaced},
  journal= {arXiv preprint arXiv:1611.04109},
  year   = {2016}
}

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submitted

R2 v1 2026-06-22T16:50:37.114Z