## Study of existence of complementary space pairs based on second order dashed lines

Prerequisites: Dashed line theory definitions and symbols Our proof strategies Proof strategy based on dashes Characterization of spaces The aim…

After almost three centuries, will we find a proof?

Prerequisites: Dashed line theory definitions and symbols Our proof strategies Proof strategy based on dashes Characterization of spaces The aim…

Prerequisite: Goldbach’s conjecture As already indicated, our ultimate goal is to use dashed line theory to prove Goldbach’s conjecture. Dashed…

The Maximum space distance calculator is a program which we developed for computing the value of the maximum distance between…

In this post we'll talk about a recursive property, that is true for all linear dashed lines with two by…

The function [latex]\mathrm{t\_value}[/latex], by definition, indicates which column of a dashed line a dash belongs to. For this reason, in…

When constructing a linear dashed line, the sequence of primes is usually used as a list of components, until it…

By now, the formula for calculation of [latex]\mathrm{t\_space}[/latex] for a linear dashed line of any order is not yet known,…

One of the open problems of dashed line theory is "characterizing" spaces, i.e. looking for a criterion that tells us…

One of the still open problems of dashed line theory is, given a linear dashed line [latex]T = (p_1, p_2,…

In this post we'll see how to obtain a formula for computing the t_space function for second order linear dashed…

In order to compute the x-th dash value in a third order linear dashed line, we can proceed in a…

In this post we'll see how it's possible to compute the x-th dash value in a second order linear dashed…

It's worth, before passing to the formulas of t_value, pausing for a while and looking closely to the moduli we…

For third order linear dashed lines, like second order ones, there exist some particular moduli which, by evaluating proper conditions,…

It may sound strange, but it's possible to compute a dash row without having an idea of its value (that…

In this post we'll talk about two fundamental properties of linear dashed lines: periodicity and symmetry. When we talk about…

Solving the downcast problem, for linear dashed lines, means finding the solution of particular equations, called "downcast characteristic equations". In…

We saw that one of the main problems of dashed line theory is computing the t, t_value and t_space functions.…

The difficulty of computing the t, t_value and t_space functions, increases as the order of the dashed line does. Their…

In the formal definition of dashed line, a dash is a couple of natural numbers (i, n), where i identifies…

A dashed line can be represented as a table having a fixed number of rows, and, potentially, infinite columns, numbered…

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