PublicationsPapers

An elementary result states that a Boolean degree 1 function on the hypercube is a dictator, and a similar result holds on the slice and on the symmetric group (a non-trivial result due to Ellis, Friedgut and Pilpel).

We explore this question on other domains. Our major result is a characterization of all Boolean degree 1 functions on the Grassmann scheme for $q=2,3,4,5$. A Boolean degree 1 function on these domains is either the indicator of a point, the indicator of a hyperplane, a combination of both, or the complement of one of the previous functions.