Related papers: An iteration based on prime and composite factors
We give a definition of higher dimensional iterated integrals based on integration over membranes. We prove basic properties of this definition and formulate a conjecture which extends Chen's de Rham Theorem for iterated integrals to the…
We define a sequence of positive integers recursively, where each term is determined as follows: starting with a given positive integer, if the term is odd, the next is the sum of its positive divisors; if the term is even, the subsequent…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…
We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The…
We introduce three simple polynomial maps with integer coefficients that have interesting dynamical properties modulo primes.
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.
The probability of finding a prime multiplet, i.e., a sequence of primes $p$ and $p+a_i$, $i=1... m$, being all primes where $p$ is some prime less than the integer $n$ is naively $1/log(n)^{m+1}$. It is shown that, in reality, it is…
Given a countable set X (usually taken to be N or Z), an infinite permutation $\pi$ of X is a linear ordering $<_\pi$ of X. This paper investigates the combinatorial complexity of infinite permutations on N associated with the image of…
In this note, we study the general form of a multiplicative bijection on several families of functions defined on manifolds, both real or complex valued. In the real case, we prove that it is essentially defined by a composition with a…
Judgment aggregation problems form a class of collective decision-making problems represented in an abstract way, subsuming some well known problems such as voting. A collective decision can be reached in many ways, but a direct one-step…
The aim of this paper is to show that there exists a deterministic algorithm that can be applied to compute the factors of a polynomial of degree 2, defined over a finite field, given certain conditions.
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
We present the pattern underlying some of the properties of natural numbers, using the framework of complex networks. The network used is a divisibility network in which each node has a fixed identity as one of the natural numbers and the…
Cluster algebras are a class of commutative algebras whose generators are defined by a recursive process called mutation. We give a brief introduction to cluster algebras, and explain how discrete integrable systems can appear in the…
The preceding paper constructed tangle machines as diagrammatic models, and illustrated their utility with a number of examples. The information content of a tangle machine is contained in characteristic quantities associated to equivalence…
A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler's recurrence based on the pentagonal numbers, but where the…
In this paper we study some structure properties of primitive weird numbers in terms of their factorization. We give sufficient conditions to ensure that a positive integer is weird. Two algorithms for generating weird numbers having a…
It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm efficiently. The…