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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
The latter also enumerates the number of unlabeled rooted trees with n + 1 vertices.
📌 3 Key Takeaways
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Objective & Hypothesis:Let n be a nonnegative integer and A = {a1, . . . , ak} be a multiset with k positive integers such that a1 ⩽ · · · ⩽ ak .
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Key Findings & Data:In this paper, we give a recursive formula for partitions and distinct partitions of positive integer n with respect to a multiset A .
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Conclusion & Impact:The latter also enumerates the number of unlabeled rooted trees with n + 1 vertices.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let n be a nonnegative integer and A = {a1, . . . , ak} be a multiset with k positive integers such that a1 ⩽ · · · ⩽ ak . In this paper, we give a recursive formula for partitions and distinct partitions of positive integer n with respect to a multiset A . We also consider the extension of the twelvefold way. By using this notion, we solve the nonintersecting circles problem, which asks to evaluate the number of ways to draw n nonintersecting circles in the plane regardless of their sizes. The latter also enumerates the number of unlabeled rooted trees with n + 1 vertices.
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Cite This Article
MANSOUR, T., MIRZVAZIRI, M., YAQUBI, D. (2022). The twelvefold way, the nonintersecting circles problem, and partitions of multisets. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 2, 765–782. https://ajindex.com/articles/607941