In this paper, we will introduce the method of intersection of -numbers for any partition  of a non-negative integer r. The results of this intersection are represented and specificated the exactly position according to a "guide value" and a "main diagram". By using the same method we will create a new way for this intersection after finding the core of each "guide".

Since James introduced the idea of an e-abacus diagram in 1978, this topic plays important roles with many topics, especially in algebra. In this paper, we will present new insights on this topic so that it appears to us as a graph theory; specifically a directed graph, according to certain conditions, to be a new start with another field. This proposed technique will be applied to the model that was approved by Mahmood and Mahmood in 2019 on English letters and to see how successful we are on Letter-Word-Sentence. It is completely natural that this method will have a new and very difficult method as an entrance to a new type of encryption process

In the past years, there have been several studies trying to link between the letters of international languages and partition theory, especially the English letters. Sami and Mahmoodin [4] used the idea for coding Syriac letters using partition theory, as shown in the following Table 1. We tried to exploit an important aspect in some of the techniques mentioned in [5-8] references.

This research is based on the idea of replacing what the sites contain in the e-abacus diagram with each other and then representing the new diagram (derived from the original diagram) and knowing the value of its partition (as a type of hidden coding of the origin of the diagram or in the sense of the opposite diagram).

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?