Replacing the Content in e-Abacus Diagram II

Abstract

In our normal life, we sometimes need a process of replacing something with another to get out of the stereotype. From this point of view, Mahmood’s attempted in the year 2020 to replace the content in the first main e-abacus diagram. He found the general rule for finding the value of the new partition after the replacement from the original partition. Here we raise the question: Can we find the appropriate mechanisms for the remainder of the main e-abacus diagram?

Adding Rows in Main e-Abacus Diagrams

“…All of these will be important for application of this topic in any subsequent study. The only note that these techniques cannot be applied to is the partition theory notation of English letters [12] or Syriac Letters [13], most of these letters do not have adjacent bead rows without any space between them and so the process will be exposed and therefore not recommended here at all.…”

On Left Slides (Upper or Lower) in e-Abacus Diagram

“…It follows that we will benefit from the use of these new patterns to understand how any word can be conveyed to a specific location and arrive there conveniently and securely. These four patterns will be useful in the coding of the English letters used by Mahmood and Mahmood [4][5], who adopted a unique form for each letter based solely on the 5-abacus diagram.…”

“…As for the non-negative integers 𝜏 1 , 𝜏 2 , … , 𝜏 𝑛 whose total equals the value r. A partition 𝜏 = (𝜏 1 , 𝜏 2 , … , 𝜏 𝑛 ) is an arrangement of these numbers that takes advantage of the fact that they are either equal or decreasing. For example, (5,5,4,4,4,4,1) is a partition of 27, but (5,4,4,4,4,5,1) is not. Defining β j = 𝜏 𝑗 + 𝑏 − 𝑗, 1 ≤ 𝑗 ≤ 𝑏.…”