Walks in the Quarter Plane with Multiple Steps
We extend the classification of nearest neighbour walks in the quarter plane to models in which multiplicities are attached to each direction in the step set. Our study leads to a small number of infinite families that completely characterize all the models whose associated group is D4, D6, or D8. T...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2015-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2463/pdf |
| _version_ | 1797270218797481984 |
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| author | Manuel Kauers Rika Yatchak |
| author_facet | Manuel Kauers Rika Yatchak |
| author_sort | Manuel Kauers |
| collection | DOAJ |
| description | We extend the classification of nearest neighbour walks in the quarter plane to models in which multiplicities are attached to each direction in the step set. Our study leads to a small number of infinite families that completely characterize all the models whose associated group is D4, D6, or D8. These families cover all the models with multiplicites 0, 1, 2, or 3, which were experimentally found to be D-finite — with three noteworthy exceptions. |
| first_indexed | 2024-04-25T02:00:47Z |
| format | Article |
| id | doaj.art-95fd695e39534776be82a4bebea945de |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:47Z |
| publishDate | 2015-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-95fd695e39534776be82a4bebea945de2024-03-07T15:01:26ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502015-01-01DMTCS Proceedings, 27th...Proceedings10.46298/dmtcs.24632463Walks in the Quarter Plane with Multiple StepsManuel Kauers0Rika Yatchak1Research Institute for Symbolic ComputationResearch Institute for Symbolic ComputationWe extend the classification of nearest neighbour walks in the quarter plane to models in which multiplicities are attached to each direction in the step set. Our study leads to a small number of infinite families that completely characterize all the models whose associated group is D4, D6, or D8. These families cover all the models with multiplicites 0, 1, 2, or 3, which were experimentally found to be D-finite — with three noteworthy exceptions.https://dmtcs.episciences.org/2463/pdfcomputer algebralattice walksd-finiteness[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Manuel Kauers Rika Yatchak Walks in the Quarter Plane with Multiple Steps Discrete Mathematics & Theoretical Computer Science computer algebra lattice walks d-finiteness [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Walks in the Quarter Plane with Multiple Steps |
| title_full | Walks in the Quarter Plane with Multiple Steps |
| title_fullStr | Walks in the Quarter Plane with Multiple Steps |
| title_full_unstemmed | Walks in the Quarter Plane with Multiple Steps |
| title_short | Walks in the Quarter Plane with Multiple Steps |
| title_sort | walks in the quarter plane with multiple steps |
| topic | computer algebra lattice walks d-finiteness [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2463/pdf |
| work_keys_str_mv | AT manuelkauers walksinthequarterplanewithmultiplesteps AT rikayatchak walksinthequarterplanewithmultiplesteps |