Capacity constraints in ball and urn distribution problems
This paper explores the distribution of indistinguishable balls into distinct urns with varying capacity constraints, a foundational issue in combinatorial mathematics with applications across various disciplines. We present a comprehensive theoretical framework that addresses both upper and lower c...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-05-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037425000561 |
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| author | Jingwei Li Thomas G. Robertazzi |
| author_facet | Jingwei Li Thomas G. Robertazzi |
| author_sort | Jingwei Li |
| collection | DOAJ |
| description | This paper explores the distribution of indistinguishable balls into distinct urns with varying capacity constraints, a foundational issue in combinatorial mathematics with applications across various disciplines. We present a comprehensive theoretical framework that addresses both upper and lower capacity constraints under different distribution conditions, elaborating on the combinatorial implications of such variations. Through rigorous analysis, we derive analytical solutions that cater to different constrained environments, providing a robust theoretical basis for future empirical and theoretical investigations. These solutions are pivotal for advancing research in fields that rely on precise distribution strategies, such as physics and parallel processing. The paper not only generalizes classical distribution problems but also introduces novel methodologies for tackling capacity variations, thereby broadening the utility and applicability of distribution theory in practical and theoretical contexts. |
| format | Article |
| id | doaj-art-979720c68b7842b2a148fa2853d9f3d3 |
| institution | Kabale University |
| issn | 2590-0374 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-979720c68b7842b2a148fa2853d9f3d32025-08-20T03:26:39ZengElsevierResults in Applied Mathematics2590-03742025-05-012610059210.1016/j.rinam.2025.100592Capacity constraints in ball and urn distribution problemsJingwei Li0Thomas G. Robertazzi1Department of Electrical and Computer Engineering, Stony Brook University, 100 Nicolls Rd, Stony Brook, 11790, NY, USACorresponding author.; Department of Electrical and Computer Engineering, Stony Brook University, 100 Nicolls Rd, Stony Brook, 11790, NY, USAThis paper explores the distribution of indistinguishable balls into distinct urns with varying capacity constraints, a foundational issue in combinatorial mathematics with applications across various disciplines. We present a comprehensive theoretical framework that addresses both upper and lower capacity constraints under different distribution conditions, elaborating on the combinatorial implications of such variations. Through rigorous analysis, we derive analytical solutions that cater to different constrained environments, providing a robust theoretical basis for future empirical and theoretical investigations. These solutions are pivotal for advancing research in fields that rely on precise distribution strategies, such as physics and parallel processing. The paper not only generalizes classical distribution problems but also introduces novel methodologies for tackling capacity variations, thereby broadening the utility and applicability of distribution theory in practical and theoretical contexts.http://www.sciencedirect.com/science/article/pii/S2590037425000561Combinatorial distributionCapacity constraintsAnalytical solutionsDistribution theory |
| spellingShingle | Jingwei Li Thomas G. Robertazzi Capacity constraints in ball and urn distribution problems Results in Applied Mathematics Combinatorial distribution Capacity constraints Analytical solutions Distribution theory |
| title | Capacity constraints in ball and urn distribution problems |
| title_full | Capacity constraints in ball and urn distribution problems |
| title_fullStr | Capacity constraints in ball and urn distribution problems |
| title_full_unstemmed | Capacity constraints in ball and urn distribution problems |
| title_short | Capacity constraints in ball and urn distribution problems |
| title_sort | capacity constraints in ball and urn distribution problems |
| topic | Combinatorial distribution Capacity constraints Analytical solutions Distribution theory |
| url | http://www.sciencedirect.com/science/article/pii/S2590037425000561 |
| work_keys_str_mv | AT jingweili capacityconstraintsinballandurndistributionproblems AT thomasgrobertazzi capacityconstraintsinballandurndistributionproblems |