Block sizes in the block sets conjecture are unbounded for alphabet size 3 but bounded by 2 for the 123 template, improving on prior tower-type bounds.
K r \'i z , Permutation groups in E uclidean R amsey T heory , Proceedings of the American Mathematical Society 112 (1991), 899 -- 907
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Block Sizes in the Block Sets Conjecture
Block sizes in the block sets conjecture are unbounded for alphabet size 3 but bounded by 2 for the 123 template, improving on prior tower-type bounds.