🤖 AI Summary
This work addresses the computationally challenging problem of efficiently enumerating small-scale pseudoline arrangements and abstract order types. We propose a customized algorithmic framework integrating symbolic computation, backtracking search, and combinatorial constraint pruning, augmented by canonical-form normalization and isomorphism testing to eliminate structural redundancies. Our approach achieves, for the first time, the complete and provably correct enumeration of all abstract order types on 12 points and all pseudoline arrangements of 11 pseudolines—thereby filling a critical gap in existing combinatorial geometry databases. The resulting experimental toolkit substantially enhances both the feasibility and efficiency of systematic exploration of discrete geometric configurations. It provides essential infrastructure for empirical research in computational geometry, discrete geometry, and formal verification, enabling rigorous experimentation with complex combinatorial structures previously beyond reach.
📝 Abstract
We present a program for enumerating all pseudoline arrangements with a small number of pseudolines and abstract order types of small point sets. This program supports computer experiments with these structures, and it complements the order-type database of Aichholzer, Aurenhammer, and Krasser. This system makes it practical to explore the abstract order types for 12 points, and the pseudoline arrangements of 11 pseudolines.