The Number of Sides of a Parallelogram
We define parallelograms of base a and b in a group. They appear as minimal relators in a presentation of a subgroup with generators a and b. In a Lie group they are realized as closed polygonal lines, with sides being orbits of left-invariant vector fields. We estimate the number of sides of parall...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
1999-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/251/pdf |
| _version_ | 1797270250764369920 |
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| author | Elisha Falbel Pierre-Vincent Koseleff |
| author_facet | Elisha Falbel Pierre-Vincent Koseleff |
| author_sort | Elisha Falbel |
| collection | DOAJ |
| description | We define parallelograms of base a and b in a group. They appear as minimal relators in a presentation of a subgroup with generators a and b. In a Lie group they are realized as closed polygonal lines, with sides being orbits of left-invariant vector fields. We estimate the number of sides of parallelograms in a free nilpotent group and point out a relation to the rank of rational series. |
| first_indexed | 2024-04-25T02:01:17Z |
| format | Article |
| id | doaj.art-f6c42667366a4c2e8bdc77f3f7582b84 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:17Z |
| publishDate | 1999-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-f6c42667366a4c2e8bdc77f3f7582b842024-03-07T14:58:15ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80501999-01-01Vol. 3 no. 210.46298/dmtcs.251251The Number of Sides of a ParallelogramElisha Falbel0Pierre-Vincent Koseleff1https://orcid.org/0000-0003-0809-5019Institut de Mathématiques de JussieuInstitut de Mathématiques de JussieuWe define parallelograms of base a and b in a group. They appear as minimal relators in a presentation of a subgroup with generators a and b. In a Lie group they are realized as closed polygonal lines, with sides being orbits of left-invariant vector fields. We estimate the number of sides of parallelograms in a free nilpotent group and point out a relation to the rank of rational series.https://dmtcs.episciences.org/251/pdflie algebrasfree groupmagnus grouplower central serieslyndon basis[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Elisha Falbel Pierre-Vincent Koseleff The Number of Sides of a Parallelogram Discrete Mathematics & Theoretical Computer Science lie algebras free group magnus group lower central series lyndon basis [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | The Number of Sides of a Parallelogram |
| title_full | The Number of Sides of a Parallelogram |
| title_fullStr | The Number of Sides of a Parallelogram |
| title_full_unstemmed | The Number of Sides of a Parallelogram |
| title_short | The Number of Sides of a Parallelogram |
| title_sort | number of sides of a parallelogram |
| topic | lie algebras free group magnus group lower central series lyndon basis [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/251/pdf |
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