On the number of inductively minimal geometries

We count the number of inductively minimal geometries for any given rank by exhibiting a correspondence between the inductively minimal geometries of rank n and the trees with n+1 vertices. The proof of this correspondence uses the van Rooij–Wilf characterization of line graphs (see [11]).

Bibliographic Details
Main Authors: Cara, Philippe, Lehman, Serge, Pasechnik, Dmitrii V.
Other Authors: School of Physical and Mathematical Sciences
Format: Journal Article
Language:English
Published: 2013
Subjects:
Online Access:https://hdl.handle.net/10356/95261
http://hdl.handle.net/10220/9272
Description
Summary:We count the number of inductively minimal geometries for any given rank by exhibiting a correspondence between the inductively minimal geometries of rank n and the trees with n+1 vertices. The proof of this correspondence uses the van Rooij–Wilf characterization of line graphs (see [11]).