Related papers: Minor-closed classes of binary functions
Given a real $n \times m$ matrix $B$, its operator norm can be defined as $$|B|=\max_{|v|=1}|Bv|.$$ We consider a matrix "small" if it has non-negative integer entries and its operator norm is less than $2$. These matrices correspond to…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
Submodular functions are well-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions,…
We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…
We introduce two types bilateral zeta functions, which are related to the primitive and normalized multiple sine functions respectively. Further, we establish their main properties, that is, Fourier expansions, analytic continuations,…
This survey provides a comprehensive overview of the study of the binary and Boolean rank from both a mathematical and a computational perspective, with particular emphasis on their relationship to the real rank. We review the basic…
Partition of unities appear in many places in analysis. Typically they are generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire…
We develop a theory of minors for alternating dimaps --- orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex. We show that…
Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…
We develop a theory of boundary functions for ideals in trivially analytic subalgebras of simple AF C*-algebras with an injective 0-cocycle, a class which includes all full nest algebras. Boundary functions are maps from the spectrum of the…
This paper studies the problem of decomposing a low-rank positive-semidefinite matrix into symmetric factors with binary entries, either $\{\pm 1\}$ or $\{0,1\}$. This research answers fundamental questions about the existence and…
We consider the problem of minimising functions represented as a difference of lattice submodular functions. We propose analogues to the SupSub, SubSup and ModMod routines for lattice submodular functions. We show that our…
Domination theory has been studied extensively in the context of binary monotone systems, where the structure function is a sum of products of the component state variables, and with coefficients given by the signed domination function.…
Let $\lambda$ be an uncountable cardinal such that $2^{< \lambda } = \lambda$. Working in the setup of generalized descriptive set theory, we study the structure of $\lambda^+$-Borel measurable functions with respect to various kinds of…
If $M$ is a matroid, then a simple matroid $M'$ with the same rank as $M$ is an adjoint of $M$ if there is an inclusion-reversing embedding $\phi$ of the lattice of flats of $M$ into the lattice of flats of $M'$ such that $\phi$ maps the…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
In this note we give some sufficient conditions for an analytic function $f(z)$ normalized by $f'(0)=1$ to belong to certain subfamilies of the class of Bazilevic functions. In earlier works, the closure property of many classes of…
We show that the class of bicircular matroids has only a finite number of excluded minors. Key tools used in our proof include representations of matroids by biased graphs and the recently introduced class of quasi-graphic matroids. We show…
Let $V$ be a finite set of size $n$. We consider real functions on the "slice" $\binom{V}{k}$, which are also known as functions in the Johnson scheme. For $I \subseteq J \subseteq V$, the characteristic function of the set of all…
In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. \ We first establish a criterion on the coprime-ness of two singular inner functions and…