## 9 Citations

Quasi-configurations: building blocks for point-line configurations

- MathematicsArs Math. Contemp.
- 2016

The motivation is the problem of the existence of $(n_4)$ configurations, still open for few remaining values of $n, which is based on quasi-configurations: point-line incidence structures where each point is incident to at least $3$ lines and each line is incidentto at least$3$ points.

Eventually, geometric $(n_{k})$ configurations exist for all $n$

- Mathematics
- 2021

In a series of papers and in his 2009 book on configurations Branko Grünbaum described a sequence of operations to produce new (n4) configurations from various input configurations. These operations…

Connected geometric (n_k) configurations exist for almost all n

- MathematicsThe Art of Discrete and Applied Mathematics
- 2021

In a series of papers and in his 2009 book on configurations Branko Grunbaum described a sequence of operations to produce new (n4) configurations from various input configurations. These operations…

Combinatorial configurations, quasiline arrangements, and systems of curves on surfaces

- MathematicsArs Math. Contemp.
- 2018

It is shown that every incidence structure (and therefore also every combinatorial configuration) can be realized as a monotone quasiline arrangement in the real projective plane.

A manifold associated to a topological (n_k) configuration

- MathematicsArs Math. Contemp.
- 2014

A non-orientable 2 -manifold associated in a natural way to a topological ( n k ) configuration in the projective plane is described, which defines an equivalence class within topological configurations.

A Greedy Algorithm to Compute Arrangements of Lines in the Projective Plane

- MathematicsDiscret. Comput. Geom.
- 2022

We introduce a greedy algorithm optimizing arrangements of lines with respect to a property. We apply this algorithm to the case of simpliciality: it recovers all known simplicial arrangements of…

Algorithms and complexity for counting configurations in Steiner triple systems

- Computer ScienceJournal of Combinatorial Designs
- 2022

General theoretical results as well as specific practical algorithms for important configurations are presented and the relevance of computational complexity and algorithms of low complexity is highlighted.

An improved lower bound for general position subset selection

- Computer Science, MathematicsInt. J. Comput. Sci. Math.
- 2017

This paper presents an algorithm for GPSS to improve this bound based on the number of collinear pairs of points, and experimentally evaluates this and few other GPSS algorithms.

## References

SHOWING 1-10 OF 17 REFERENCES

Enumerating topological $(n_k)$-configurations

- MathematicsCCCG 2011
- 2011

This work provides an algorithm for generating, for given $n and $k$, all topological $(n_k)$-configurations up to combinatorial isomorphism, without enumerating first all combinatorsial $(n-k) $- configurations.

) Configurations Exist for Almost All N –– an Update

- Mathematics

An (n k) configuration is a family of n points and n (straight) lines in the Euclidean plane such that each point is on precisely k of the lines, and each line contains precisely k of the points. A…

Configurations of Points and Lines

- Art
- 2009

This is the only book on the topic of geometric configurations of points and lines. It presents in detail the history of the topic, with its surges and declines since its beginning in 1876. It covers…

There are no realizable 15_4- and 16_4-configurations.

- Mathematics
- 2005

There exist a finite number of natural numbers n for which we do not know whether a realizable n4-configuration does exist. We settle the two smallest unknown cases n = 15 and n = 16. In these cases…

On the finite set of missing geometric configurations (n4)

- Mathematics, Computer ScienceComput. Geom.
- 2013

The combinatorial (19_4) configurations

- MathematicsArs Math. Contemp.
- 2012

It is proved that two of the combinatorial (19 4 ) configurations are not geometrically realizable over any field, and the computation of the 971 171 combinatorsial (18 4) configurations which lacked an independent verification is confirmed.

The combinatorial (194) configurations

- Mathematics
- 2012

A parallel backtrack search is carried out to classify, up to isomorphism, all combinatorial (194) configurations. A total of 269224653 such configurations were found. We prove that two of the…

Technische Universität Darmstadt E-mail address: juergen.bokowski@gmail.com (V. Pilaud) CNRS & LIX, ´ Ecole Polytechnique, Palaiseau E-mail address

- Technische Universität Darmstadt E-mail address: juergen.bokowski@gmail.com (V. Pilaud) CNRS & LIX, ´ Ecole Polytechnique, Palaiseau E-mail address