On the Generation of Rank 3 Simple Matroids with an Application to Terao's Freeness Conjecture

DOI10.1137/19M1296744zbMath1465.05025arXiv1907.01073WikidataQ123190732 ScholiaQ123190732MaRDI QIDQ4992840

Christopher Jefferson, Reimer Behrends, Mohamed Barakat, Lukas Kühne, Martin Leuner

Publication date: 10 June 2021

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.01073

zbMATH Keywords

priority queueNoSQL databaseArangoDBintegrally splitting characteristic polynomialiterator of leaves of rooted treeleaf-iteratorparallel evaluation of recursive iteratorrank 3 simple matroidsrecursive iteratorTerao's freeness conjecturetree-iterator

Mathematics Subject Classification ID

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Combinatorics in computer science (68R05) Parallel algorithms in computer science (68W10) Relations with arrangements of hyperplanes (32S22) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Combinatorial aspects of matroids and geometric lattices (05B35)

Related Items

Logarithmic vector fields and freeness of divisors and arrangements: new perspectives and applications. Abstracts from the workshop held January 24--30, 2021 (online meeting) ⋮ On the geometry of flag Hilbert-Poincaré series for matroids ⋮ On the geometry of flag Hilbert-Poincaré series for matroids ⋮ On nearly free arrangements of lines with nodes and triple points ⋮ Unexpected curves in \(\mathbb{P}^2\), line arrangements, and minimal degree of Jacobian relations ⋮ Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture

Uses Software

• GAP
• homalg
• SINGULAR
• GitHub
• CAP
• ModulePresentationsForCAP
• LinearAlgebraForCAP
• GeneralizedMorphismsForCAP
• ZariskiFrames
• ArangoDB

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-recursive freeness and non-rigidity
• Divisionally free arrangements of hyperplanes
• Minimal fields of definition for simplicial arrangements in the real projective plane
• Recursively free reflection arrangements
• Matroid enumeration for incidence geometry
• Free arrangements of hyperplanes and supersolvable lattices
• Generalized exponents of a free arrangement of hyperplanes and Shepherd- Todd-Brieskorn formula
• Permutation group algorithms based on partitions. I: Theory and algorithms
• Restrictions of free arrangements and the division theorem
• Minimal and canonical images
• New refiners for permutation group search
• Geometric algebra for combinatorial geometries
• On inductively free reflection arrangements.
• Graphs whose flow polynomials have only integral roots
• Freeness for 13 lines arrangements is combinatorial
• Supersolvable lattices
• On matroids determined by their Tutte polynomials
• Logarithmic bundles and line arrangements, an approach via the standard construction
• AN AXIOMATIC SETUP FOR ALGORITHMIC HOMOLOGICAL ALGEBRA AND AN ALTERNATIVE APPROACH TO LOCALIZATION
• Roots of characteristic polynomials and intersection points of line arrangements
• A Decomposition for Combinatorial Geometries
• Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture