Abstract

Combinatorics is a fundamental field in the high school math curricula of most countries worldwide, including Vietnam and the United States. It stems from basic concepts of sets of elements, mapping functions, combinations, permutations, and others to problems of listing all binary sequences of n elements, listing all r-combinations of n elements, listing all permutations of n elements. These combinatorial problems assisted with programming languages and machine learning models (emerging machine learning (ML)) have processed numerous applications in various areas of modern life, especially rare diseases as defined by the United States and the European Union. There are different disease-causing variants of rare diseases, so they need to be simulated to come up with appropriate treatment plans. In this paper, a specific synthetic mathematical model which is the problem of listing permutations on many pathogenic variants to simulate pathogenic factors is constructed. It is hoped that the result of this study can provide some suggestion for rare disease prevention and treatments.

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