When entropy meets Tur\'an: new proofs and hypergraph Tur\'an results
Ting-Wei Chao, Hung-Hsun Hans Yu

TL;DR
This paper introduces entropy-based proofs for Turán's theorem, explores connections between entropic measures and hypergraph properties, and determines Turán densities for new hypergraph families called tents.
Contribution
It provides a novel entropic proof of a density version of Turán's theorem and determines Turán densities for tents, extending previous hypergraph results.
Findings
Entropy-based formulation of Turán's theorem
Connection between entropic quantities and hypergraph spectral measures
Turán density determined for tents hypergraphs
Abstract
In this paper, we provide a new proof of a density version of Tur\'an's theorem. We also rephrase both the theorem and the proof using entropy. With the entropic formulation, we show that some naturally defined entropic quantity is closely connected to other common quantities such as Lagrangian and spectral radius. In addition, we also determine the Tur\'an density for a new family of hypergraphs, which we call tents. Our result can be seen as a new generalization of Mubayi's result on the extended cliques.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Computability, Logic, AI Algorithms
