Related papers: A Combinatorial Approach to Positional Number Syst…
In this paper, we prove several theorems on systems of polynomials with at least one positive real zero based on the theory of conceive polynomials. These theorems provide sufficient conditions for systems of multivariate polynomials…
Large sets of combinatorial designs has always been a fascinating topic in design theory. These designs form a partition of the whole space into combinatorial designs with the same parameters. In particular, a large set of block designs,…
Two dimensional matrices with binary (0/1) entries are a common data structure in many research fields. Examples include ecology, economics, mathematics, physics, psychometrics and others. Because the columns and rows of these matrices…
We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string…
We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…
This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…
A new construction of the real number system, that is built directly upon the additive group of integers and has its roots in the definition due to Henri Poincar\'e of the rotation number of an orientation preserving homeomorphism of the…
We consider the problem of approaching real numbers with rational numbers with prime denominator and with a single numerator allowed for each denominator. We then present a simple application, related to possible correlations between trace…
In this work, we established symmetric representation of numbers where one can use any of 9 digits giving the same number. The representations of natural numbers from 0 to 1000 are given using only single digit in all the nine cases, i.e.,…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
This article describes a technique of using a trigonometric function and combinatorial calculations to code or transform any finite sequence of binary numbers (0s and 1s) of any length to a unique set of three Real numbers. In reverse,…
This paper introduces a binary encoding that supports arbitrarily large, small and precise decimals. It completely preserves information and order. It does not rely on any arbitrary use-case-based choice of calibration and is readily…
In additive number theory, a finite set $A$ of integers is an $h$-basis for $n$ if every integer in $\{0,1,2,\ldots, n\}$ can be represented as the sum of exactly $h$ not necessarily distinct elements of $A$. This paper introduces a new…
Throughout history, recreational mathematics has always played a prominent role in advancing research. Following in this tradition, in this paper we extend some recent work with crazy sequential representations of numbers- equations made of…
This work is meant to demonstrate new class of prime numbers -- cyclic prime numbers, that can be derived from any prime number at certain numeric systems. Cyclic prime numbers are also related to the cyclic numbers and full reptend prime…
In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class…
We propose a new method to construct a stationary process and random field with a given decreasing covariance function and any one-dimensional marginal distribution. The result is a new class of stationary processes and random fields. The…
We produce combinatorial models for configuration space in a simplicial complex, and for configurations near a single point ("local configuration space.") The model for local configuration space is built out of the poset of poset structures…
The signed-bit representation of real numbers is like the binary representation, but in addition to 0 and 1 you can also use -1. It lends itself especially well to the constructive (intuitionistic) theory of the real numbers. The first part…
In the present article, modeling certain rational numbers, that are represented in terms of Cantor series, are described. The statements on relations between digits in the representations of rational numbers by Cantor series (for the case…