## 14. A recursive property of linear dashed lines with two by two coprime components

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

## Factorization dashed lines

Prerequisites: Our proof strategies Periodicity and symmetry in linear dashed lines When constructing a linear dashed line, the sequence of…

## Calculation of t_space for dashed lines of arbitrary order

Prerequisites: Computation of spaces in second order linear dashed lines Inclusion-exclusion principle (preferential) By now, the formula for calculation of…

## Characterization of spaces

Prerequisites: Dashed line theory definitions and symbols Computation of a dash value in a linear third order dashed line Computation…

## 13. Computation of spaces in second order linear dashed lines

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

## 12. Computation of a dash value in a linear third order dashed line

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

## 11. Computation of a dash value in a linear second order dashed line

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

## 10. Row computation and differences between dash values

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

## 9. Row computation in third order linear dashed lines

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

## 8. Row computation in second order linear dashed lines

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

## 3. Periodicity and symmetry in linear dashed lines

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

## 7. Downcast characteristic equations of t and t_value for linear dashed lines

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

## 5. First order linear dashed lines

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

## 6. The downcast problem

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

## 2. Dashed lines, dashes and spaces: some definitions and simple properties

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

## 1. From prime numbers to dashed lines

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