I will present a fully polynomial-time approximation scheme (FPTAS) to count the number of q-colorings for k-uniform hypergraphs with maximum degree D if k>=28 and q>315D^{14/(k?14)}, as well as an accompanying sampling algorithm with slightly worse conditions. These are the first approximate counting and sampling algorithms in the regime q<<? (for large ? and k) without any additional assumptions. In these regimes, frozen colourings are present, forming an obstacle to the standard Markov chain Monte Carlo approach. Instead, our method is based on the recent work of Moitra (STOC, 2017), in which Lovasz Local Lemma is the key ingredient. Joint work with Chao Liao, Pinyan Lu, Chihao Zhang.

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