Let f:{0, 1} n→{0, 1} be a boolean function, and let f∧(x, y)= f (x∧ y) denote the AND-function
of f, where x∧ y denotes bit-wise AND. We study the deterministic communication …

We extend the definitions of complexity measures of functions to domains such as the
symmetric group. The complexity measures we consider include degree, approximate …

Let $\mathscr {F} _ {n, d} $ be the class of all functions $ f:\{-1, 1\}^ n\to [-1, 1] $ on the $ n $-
dimensional discrete hypercube of degree at most $ d $. In the first part of this paper, we …

We investigate the existence of Boolean degree $ d $ functions on the Grassmann graph of
$ k $-spaces in the vector space $\mathbb {F} _q^ n $. For $ d= 1$ several non-existence …

arXiv:2203.04760v2 [math.CO] 14 Mar 2022 Page 1 arXiv:2203.04760v2 [math.CO] 14 Mar
2022 Junta threshold for low degree Boolean functions on the slice Yuval Filmus March 15 …

We propose a new paradigm for studying the structure of Boolean functions on the biased
Boolean hypercube, ie when the measure is µp and p is potentially very small, eg as small …

We generalize and extend the ideas in a recent paper of Chiarelli, Hatami and Saks to prove
new bounds on the number of relevant variables for boolean functions in terms of a variety of …

Abstract The Fourier-Walsh expansion of a Boolean function f: 0, 1 n→ 0, 1 is its unique
representation as a multilinear polynomial. The Kindler-Safra theorem (2002) asserts that if …

A perfect k-coloring of the Boolean hypercube Q n is a function from the set of binary words
of length n onto a k-set of colors such that for any colors i and j every word of color i has …

This thesis consists of three disparate parts. In the first, we generalize and extend recent
ideas of Chiarelli, Hatami and Saks to obtain new bounds on the number of relevant …