Dictatorships and juntas in the symmetric group
Seminar Room 1, Newton Institute
One of the main themes of using discrete harmonic analysis in combinatorial settings, is detecting structures, (or functions) that essentially depend on few coordinates. The Fourier characterization of these juntas is usually expressed by the fact that the Fourier transform is concentrated on low levels.
In this talk I will study the question of the analog of this phenomenon in the symmetric group.