American Mathematical Monthly
Concrete Math
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The Diverse factorial operators is an original study developed by the first author in the mathematical domain, it is similar to the ordinary Factorial numbers (n!) but it is more sophisticated and more general than the former. The Diverse factorial operators will be encountered in many different areas of mathematics, notably in combinatorics, algebra and mathematical analysis. The main idea of introducing the Diverse factorial operation is to replace the operation (*) between numbers by another operation, such as (*, +, -, and /). For example, n!∧(+) is equal to n+(n-1)+(n-2)+(n-3)...+1, the same thing can be applied for the other operators. Moreover, the Diverse factorial operators is not limited to introducing only different operators, but it is designed to change the sequence of the operational numbers, for example, n!∧(i+) is equal to n+(n-1*i)+(n- 2*i)+(n-3*i)...(n-j*i), with j. In Addition, there is a rising up factorial operators which is the inverse of the normal factorial operator, for example, n↑∧(+) is equal to n+(n+1)+(n+2)+(n+3)...+(n+m), more details about these new definitions are developed in this paper. Moreover the first author has developed many definitions that might be very useful to be applied in mathematics or any other scientific domain.