切片上低次布尔函数的军政府阈值

IF 0.7 4区数学 Q2 MATHEMATICS

Electronic Journal of Combinatorics Pub Date : 2023-03-24 DOI:10.37236/11115

Yuval Filmus

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引用次数: 0

摘要

我们证明了切片$\binom{[n]}{k}$上的布尔度$d$函数是$k \geq 2d$的一个军政府，并且这个界是尖锐的。我们证明了对于任意有限$A$的$A$值度$d$函数和无限类似的切片上的函数的类似结果。

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Junta Threshold for Low Degree Boolean Functions on the Slice

We show that a Boolean degree~$d$ function on the slice $\binom{[n]}{k}$ is a junta if $k \geq 2d$, 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.

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来源期刊

Electronic Journal of Combinatorics 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

212

审稿时长

3-6 weeks

期刊介绍： The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.