Skip to Main content Skip to Navigation
Journal articles

The Number of Sides of a Parallelogram

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [6 references]  Display  Hide  Download
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Submitted on : Thursday, March 13, 2014 - 4:47:39 PM
Last modification on : Monday, December 14, 2020 - 9:41:56 AM
Long-term archiving on: : Friday, June 13, 2014 - 11:56:24 AM


Files produced by the author(s)


  • HAL Id : hal-00958925, version 1


Elisha Falbel, Pierre-Vincent Koseleff. The Number of Sides of a Parallelogram. Discrete Mathematics and Theoretical Computer Science, DMTCS, 1999, 3 (2), pp.33-42. ⟨hal-00958925⟩



Record views


Files downloads