Asymptotics of Smallest Component Sizes in Decomposable Combinatorial Structures of Alg-Log Type
A decomposable combinatorial structure consists of simpler objects called components which by thems elves cannot be further decomposed. We focus on the multi-set construction where the component generating function C(z) is of alg-log type, that is, C(z) behaves like c + d(1 -z/rho)(alpha) (ln1/1-z/r...
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Discrete Mathematics & Theoretical Computer Science
2010-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/503/pdf |
| _version_ | 1827323858488655872 |
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| author | Li Dong Zhicheng Gao Daniel Panario Bruce Richmond |
| author_facet | Li Dong Zhicheng Gao Daniel Panario Bruce Richmond |
| author_sort | Li Dong |
| collection | DOAJ |
| description | A decomposable combinatorial structure consists of simpler objects called components which by thems elves cannot be further decomposed. We focus on the multi-set construction where the component generating function C(z) is of alg-log type, that is, C(z) behaves like c + d(1 -z/rho)(alpha) (ln1/1-z/rho)(beta) (1 + o(1)) when z is near the dominant singularity rho. We provide asymptotic results about the size of thes mallest components in random combinatorial structures for the cases 0 < alpha < 1 and any beta, and alpha < 0 and beta=0. The particular case alpha=0 and beta=1, the so-called exp-log class, has been treated in previous papers. We also provide similar asymptotic estimates for combinatorial objects with a restricted pattern, that is, when part of its factorization patterns is known. We extend our results to include certain type of integers partitions. partitions |
| first_indexed | 2024-04-25T01:59:21Z |
| format | Article |
| id | doaj.art-2f6bef67eb644f99b0a85cacf2867cea |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:59:21Z |
| publishDate | 2010-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-2f6bef67eb644f99b0a85cacf2867cea2024-03-07T15:15:53ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502010-01-01Vol. 12 no. 210.46298/dmtcs.503503Asymptotics of Smallest Component Sizes in Decomposable Combinatorial Structures of Alg-Log TypeLi DongZhicheng Gao0Daniel Panario1https://orcid.org/0000-0003-3551-4063Bruce Richmond2School of Mathematics and Statistics [Ottawa]School of Mathematics and Statistics [Ottawa]Department of Combinatorics and OptimizationA decomposable combinatorial structure consists of simpler objects called components which by thems elves cannot be further decomposed. We focus on the multi-set construction where the component generating function C(z) is of alg-log type, that is, C(z) behaves like c + d(1 -z/rho)(alpha) (ln1/1-z/rho)(beta) (1 + o(1)) when z is near the dominant singularity rho. We provide asymptotic results about the size of thes mallest components in random combinatorial structures for the cases 0 < alpha < 1 and any beta, and alpha < 0 and beta=0. The particular case alpha=0 and beta=1, the so-called exp-log class, has been treated in previous papers. We also provide similar asymptotic estimates for combinatorial objects with a restricted pattern, that is, when part of its factorization patterns is known. We extend our results to include certain type of integers partitions. partitionshttps://dmtcs.episciences.org/503/pdfdecomposable structuresrestricted patternlabeled and unlabeled structuresgenerating functionsalg-logtype[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Li Dong Zhicheng Gao Daniel Panario Bruce Richmond Asymptotics of Smallest Component Sizes in Decomposable Combinatorial Structures of Alg-Log Type Discrete Mathematics & Theoretical Computer Science decomposable structures restricted pattern labeled and unlabeled structures generating functions alg-logtype [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Asymptotics of Smallest Component Sizes in Decomposable Combinatorial Structures of Alg-Log Type |
| title_full | Asymptotics of Smallest Component Sizes in Decomposable Combinatorial Structures of Alg-Log Type |
| title_fullStr | Asymptotics of Smallest Component Sizes in Decomposable Combinatorial Structures of Alg-Log Type |
| title_full_unstemmed | Asymptotics of Smallest Component Sizes in Decomposable Combinatorial Structures of Alg-Log Type |
| title_short | Asymptotics of Smallest Component Sizes in Decomposable Combinatorial Structures of Alg-Log Type |
| title_sort | asymptotics of smallest component sizes in decomposable combinatorial structures of alg log type |
| topic | decomposable structures restricted pattern labeled and unlabeled structures generating functions alg-logtype [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/503/pdf |
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