Related papers: Fixes of permutations acting on monotone Boolean f…

Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…

Monotone Boolean functions are a structurally important class of Boolean functions, but their restricted form imposes strong limitations on achievable nonlinearity. In this paper, we investigate whether evolutionary computation can evolve…

We prove two conjectures on correlation inequalities for functions that are linear combinations of unimodal Boolean monotone nondecreasing functions

We extend Stanley's work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting…

We study the most-informative Boolean function conjecture using a differential equation approach. This leads to a formulation of a functional inequality on finite-dimensional random variables. We also develop a similar inequality in the…

Permutations in the image of the pop-stack operator are said to be pop-stacked. We give a polynomial-time algorithm to count pop-stacked permutations up to a fixed length and we use it to compute the first 1000 terms of the corresponding…

A real arithmetic function f is multiplicatively monotonous if f (mn) -- f (m) has constant sign for m, n positive integers. Properties and examples of such functions are discussed, with applications to positive hermitian…

We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…

Let $V_n$ be the number of equivalence classes of invertible maps from $\{0,1\}^n$ to $\{0,1\}^n$, under action of permutation of variables on domain and range. So far, the values $V_n$ have been known for $n\le 6$. This paper describes the…

We consider the Sobolev norms of the pointwise product of two functions, and estimate from above and below the constants appearing in two related inequalities.

We bound the number of permutations with a fixed number $r$ of $321 \ominus p_0$ patterns by a constant times the number of permutations which avoid $321 \ominus p_0$. We use this new upper bound to show that the ordinary generating…

Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained…

We give a $\mathrm{poly}(\log n, 1/\epsilon)$-query adaptive algorithm for testing whether an unknown Boolean function $f: \{-1,1\}^n \to \{-1,1\}$, which is promised to be a halfspace, is monotone versus $\epsilon$-far from monotone. Since…

Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued…

This work presents a study of perturbations of symmetric Boolean functions. In particular, it establishes a connection between exponential sums of these perturbations and Diophantine equations of the form $$ \sum_{l=0}^n \binom{n}{l}…

We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…

Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these…

One matrix structure in the area of monotone Boolean functions is defined here. Some of its combinatorial, algebraic and algorithmic properties are derived. On the base of these properties, three algorithms are built. First of them…

Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of…

We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.