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arXiv · 2107.00550

Rectilinear approximation and volume estimates for hereditary bodies via [0,1]-decorated containers

Victor Falgas-Ravry·Robert Hancock·Johanna Strömberg·Andrew Uzzell
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Abstract

We use the hypergraph container theory of Balogh--Morris--Samotij and Saxton--Thomason to obtain general rectilinear approximations and volume estimates for sequences of bodies closed under certain families of projections. We give a number of applications of our results, including a multicolour generalisation of a theorem of Hatami, Janson and Szegedy on the entropy of graph limits. Finally, we raise a number of questions on geometric and analytic approaches to containers.

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Victor Falgas-Ravry, Robert Hancock, Johanna Strömberg, Andrew Uzzell. 2021-07-01. Rectilinear approximation and volume estimates for hereditary bodies via [0,1]-decorated containers. https://arxiv.org/abs/2107.00550

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