Junta Threshold for Low Degree Boolean Functions on the Slice
نویسندگان
چکیده
We show that a Boolean degree~$d$ function on the slice $\binom{[n]}{k}$ is junta if $k \geq 2d$, and this bound sharp. prove similar result for $A$-valued functions arbitrary finite $A$, an infinite analog of slice.
منابع مشابه
Boolean constant degree functions on the slice are juntas
We show that a Boolean degree d function on the slice ([n] k ) = {(x1, . . . , xn) ∈ {0, 1} : ∑n i=1 xi = k} is a junta, assuming that k, n − k are large enough. This generalizes a classical result of Nisan and Szegedy on the hypercube. Moreover, we show that the maximum number of coordinates that a Boolean degree d function can depend on is the same on the slice and the hypercube.
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ژورنال
عنوان ژورنال: Electronic Journal of Combinatorics
سال: 2023
ISSN: ['1077-8926', '1097-1440']
DOI: https://doi.org/10.37236/11115