Some generalizations of the number of placements with repetitions and various restrictions are considered. Counting these combinatorial numbers leads to the definition of nonnegative solutions of systems of linear Diophantine equations under appropriate additional restrictions. Generating functions and integral formulas for calculating input combinatorial numbers are obtained, and various problems that are solved with their application are discussed.
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- Title Formalization of combinatorial numbers in terms of entire solutions of systems of linear diophan-tine equations
- Headline Formalization of combinatorial numbers in terms of entire solutions of systems of linear diophan-tine equations
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Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 7 (Приложение)
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Keywords
combinatorial numbers, systems of linear Diophantine equations, generating functions, комбинаторные числа, системы линейных диофантовых уравнений, производящие функцииAuthors
References
Яблонский С. В. Введение в дискретную математику. М.: Наука, 1986. 384 с.
Гоцуленко В. В. Формула для числа сочетаний с повторениями при ограничениях и её применение // Прикладная дискретная математика. 2013. №2(20). С. 71-77.
Formalization of combinatorial numbers in terms of entire solutions of systems of linear diophan-tine equations | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2014. № 7 (Приложение).
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