Combinatorial properties of holographic entropy inequalities

• URL: http://arxiv.org/abs/2601.09987v1
• Date: Thu, 15 Jan 2026 02:00:00 GMT
• Title: Combinatorial properties of holographic entropy inequalities
• Authors: Guglielmo Grimaldi, Matthew Headrick, Veronika E. Hubeny, Pavel Shteyner,
• Abstract summary: A holographic entropy inequality (HEI) is a linear inequality obeyed by RyuTakayanagi holographic entanglement entropies.<n>We establish a new framework for studying HEIs, and use it to prove several properties they share.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A holographic entropy inequality (HEI) is a linear inequality obeyed by Ryu-Takayanagi holographic entanglement entropies, or equivalently by the minimum cut function on weighted graphs. We establish a new combinatorial framework for studying HEIs, and use it to prove several properties they share, including two majorization-related properties as well as a necessary and sufficient condition for an inequality to be an HEI. We thereby resolve all the conjectures presented in [arXiv:2508.21823], proving two of them and disproving the other two. In particular, we show that the null reduction of any superbalanced HEI passes the majorization test defined in [arXiv:2508.21823], thereby providing strong new evidence that all HEIs are obeyed in time-dependent holographic states.

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