On the combinatorial structure of arrangements of oriented pseudocircles
type: Item
instance of: scholarly article
title: On the combinatorial structure of arrangements of oriented pseudocircles
zbMATH Open document ID: 1053.52030
author: Ronald Ortner
author: Johann Linhart
published in: The Electronic Journal of Combinatorics
publication date: 2004-10-13T00:00:00Z
full work available at URL: https://eudml.org/doc/124059
full work available at URL: v11i1r30.html
review text: Summary: We introduce intersection schemes (a generalization of uniform oriented matroids of rank 3) to describe the combinatorial properties of arrangements of pseudocircls in the plane and on closed orientable surfaces. Similar to the Folkman-Lawrence topological representation theorem for oriented matroids we show that there is a one-to-one correspondence between intersection schemes and equivalence classes of arrangements of pseudocircles. Furthermore, we consider arrangements where the pseudocircles separate the surface into two components. For these strict arrangements there is a one-to-one correspondence to a quite natural subclass of consistent intersection schemes.
Mathematics Subject Classification ID: 52C30
Mathematics Subject Classification ID: 52C40
zbMATH DE Number: 2107472
zbMATH Keywords: intersection schemes
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2107472