FKN theorem for the multislice, with applications

Yuval Filmus

The multislice is a generalization of the slice to several colors.

We prove a Friedgut–Kalai–Naor theorem for balanced multislices. Our proof is inductive, and uses as a base case our Friedgut–Kalai–Naor theorem for balanced slices.

As an application, we prove stability versions of the edge-isoperimetric inequality for the multislices for settings of parameters in which the optimal set depends on a single coordinate.


 author = {Yuval Filmus},
 title = {{FKN} theorem for the multislice, with applications},
 journal = {Combinatorics, Probability and Counting},
 volume = {29},
 number = {2},
 year = {2020},
 pages = {200--212}
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