2021/07/01 by Falgas-Ravry, Victor, Hancock, Robert, Strömberg, Johanna +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2107.00550
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.