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?

Since the appearance of Young’s diagram, it has played a fundamental and pivotal role in many fields of mathematics, perhaps the most prominent of which is algebra, graph theory, number theory…etc, and many closely related relationships, perhaps among them The most prominent is called conjugation. Many people try to find a mathematical method to find the value of the hash value in its conjugated form. Here, we will propose two new methods for the same purpose.