Discrete Mathematics & Theoretical Computer Science
Volume 3 n° 2 (1999), pp. 33-42
author: | Elisha Falbel and Pierre-Vincent Koseleff |
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title: | The Number of Sides of a Parallelogram |
keywords: | Lie algebras, free group, Magnus group, lower central series, Lyndon basis |
abstract: | 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. |
reference: | Elisha Falbel and Pierre-Vincent Koseleff (1999), The Number of Sides of a Parallelogram, Discrete Mathematics and Theoretical Computer Science 3, pp. 33-42 |
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Automatically produced on Thu Jan 21 10:14:11 MET 1999 by gustedt