3 papers
math.CO2026
Non-simple Arrangements of Lines and Pseudolines with Many Triangles
Roman Parpalak, Denis Utkin
We study affine arrangements of an even number of lines and pseudolines with many triangles. For simple ones, Blanc's bound limits the number of triangular faces to $\lfloor n(…
math.CO2026
Enumeration and Classification of Triangle-Maximal Pseudoline Arrangements
Roman Parpalak, Denis Utkin
We describe algorithms for the exhaustive enumeration and classification of simple arrangements of pseudolines ( odd) maximizing the number of triangular faces. The depth-fi…
math.CO2026
The Triangle-Maximal Series of Straight Lines
Roman Parpalak, Denis Utkin
Given lines in general position in the plane, how many bounded triangular faces can the arrangement have? We construct a straight-line affine arrangement of lines satisfyi…