PublicationsPapers

We extend the theory of complexity measures of functions beyond the Boolean cube, to domains such as the symmetric group. We show that complexity measures such as degree, approximate degree, decision tree complexity, certificate complexity, block sensitivity and sensitivity are all polynomially related for many of these domains.

In addition, we characterize Boolean degree 1 functions on the perfect matching scheme, and simplify the proof of uniqueness for $t$-intersecting families of permutations and perfect matchings.

The original motivation behind this work was determining the structure of Boolean degree d functions on the symmetric group. A concise description of this result appears here.