Junta threshold for low degree Boolean functions on the slice

03/09/2022

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by   Yuval Filmus, et al.

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We show that a Boolean degree d function on the slice [n]k is a junta if k ≥ 2d, and that this bound is sharp. We prove a similar result for A-valued degree d functions for arbitrary finite A, and for functions on an infinite analog of the slice.