Related papers: ZFC independence and subset sum

Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the same…

We study real numbers defined by multidimensional automatic arrays weighted by multiplicatively independent bases. Let $a_1, \dots, a_r\geq 2$ be integers such that $\log a_1, \dots, \log a_r$ are $\mathbb Q$-linearly independent. Given…

In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an…

We give the first analysis of the computational complexity of {\it coalition structure generation over graphs}. Given an undirected graph $G=(N,E)$ and a valuation function $v:2^N\rightarrow\RR$ over the subsets of nodes, the problem is to…

Adjacency polytopes, a.k.a. symmetric edge polytopes, associated with undirected graphs have been defined and studied in several seemingly independent areas including number theory, discrete geometry, and dynamical systems. In particular,…

Using Kripke models, it is shown that CZF does not prove Power Set, and that CZF with Subset Collection substituted by Exponentiation does not prove Subset Collection.

Combinatorial rigidity theory seeks to describe the rigidity or flexibility of bar-joint frameworks in R^d in terms of the structure of the underlying graph G. The goal of this article is to broaden the foundations of combinatorial rigidity…

The independence density of a finite hypergraph is the probability that a subset of vertices, chosen uniformly at random contains no hyperedges. Independence densities can be generalized to countable hypergraphs using limits. We show that,…

We give lower bounds for the degree of multiplicative combinations of iterates of rational functions (with certain exceptions) over a general field, establishing the multiplicative independence of said iterates. This leads to a…

We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as…

We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible…

We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include…

We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…

We suggest a combinatorial classification of metric filtrations in measure spaces; a complete invariant of such a filtration is its combinatorial scheme, a measure on the space of hierarchies of the group~$\mathbb Z$. In turn, the notion of…

We study the mean square of sums of the $k$th divisor function $d_k(n)$ over short intervals and arithmetic progressions for the rational function field over a finite field of $q$ elements. In the limit as $q\rightarrow\infty$ we establish…

Counting independent sets in graphs and hypergraphs under a variety of restrictions is a classical question with a long history. It is the subject of the celebrated container method which found numerous spectacular applications over the…

We generalize and unify the proofs of several results on algebraic in- dependence of arithmetic functions and Dirichlet series by a theorem of Ax on differential Schanuel conjecture. Along the way, we find counter-examples to some results…

In recent years, there have been intense research efforts to develop efficient methods for probabilistic inference in probabilistic influence diagrams or belief networks. Many people have concluded that the best methods are those based on…

We build on recent work of Yeats, Courtiel, and others involving connected chord diagrams. We first derive from a Hopf-algebraic foundation a class of tree-like functional equations and prove that they are solved by weighted generating…

We investigate the existence of a class of ZFC-provably total recursive unary functions, given certain constraints, and apply some of those results to show that, for $\Sigma_1$-sound set theory, ZFC$\not\vdash P<NP$.