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We present a unified framework to asymptotically count the number of sets, with a given cardinality, free of certain configurations. This is done by combining the hypergraph containers methodology joint with arithmetic removal lemmas. Several applications involving linear configurations are described, as well as some applications in the random sparse setting.
CitacióRue, J., Serra, O., Vena , L. Counting configuration–free sets in groups. A: European Conference on Combinatorics, Graph Theory and Applications. "Eurocomb 2015". Bergen: 2015, p. 549-557.