Geodesic
Junta threshold for low degree Boolean functions on the slice
Yuval Filmus1
1Technion - Israel Institute of Technology
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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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.
DOI : 10.37236/11115
Classification : 94D10, 06E30
Mots-clés : low degree Boolean functions

Yuval Filmus  1

1 Technion - Israel Institute of Technology 
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Yuval Filmus. Junta threshold for low degree Boolean functions on the slice. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11115

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