Various generalizations of the concept of combination with repetitions are obtained. Formulas for the calculation of the considered combinatorial numbers are found, and various problems that are solved with their application are considered.
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- Title A formula for the number of combinations with constrained repetitions and its application
- Headline A formula for the number of combinations with constrained repetitions and its application
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Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 2(20)
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Keywords
multisets, generating functions, Diophantine equations, formal polynomial, combinations with constrained repetitions, мультимножества, производящие функции, формальный полином, диофантовы уравнения, сочетания с повторениями при ограниченияхAuthors
References
Полиа Г., Сеге Г. Задачи и теоремы из анализа. М.: Наука, 1978. 391 с.
Заторский Р. А. Подсчет m-подмультимножеств через их вторичные спецификации // Комбинаторный анализ. Вып. 7. М.: МГУ, 1986. С. 136-145.
Juric Z. and Siljak H. A new formula for the number of combinations and permutations of multisets // Appl. Math. Sci. 2011. V. 5. No. 18. P. 875-881.
MacMahon P. A. Combinatory analysis. Cambridge: The University Press, 1915. 296 p.
Петровский А. Б. Пространства множеств и мультимножеств. М.: УРСС, 2003. 248 с.
Новиков Ф. А. Дискретная математика для программистов. СПб.: Питер, 2009. 384 с.
Виленкин Н. Я. Комбинаторика. М.: Наука, 1969. 323 с.
A formula for the number of combinations with constrained repetitions and its application | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2013. № 2(20).
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