On Matroids and Linearly Independent Set Families
Giuliano G. La Guardia, Luciane Grossi, Welington Santos
TL;DR
This paper introduces new matroid families derived from linearly independent set families, generalizing vectorial matroids over a field, thus expanding the theoretical framework of matroid theory.
Contribution
The paper constructs new matroid families based on LISFs, extending the class of vectorial matroids and providing a broader theoretical foundation.
Findings
New matroid families are constructed from LISFs.
The construction generalizes vectorial matroids.
The work broadens the theoretical understanding of matroids.
Abstract
New families of matroids are constructed in this note. These new fami- lies are derived from the concept of linearly independent set family (LISF) introduced by Eicker and Ewald [Linear Algebra and its Applications 388 (2004) 173-191]. The proposed construction generalizes in a natural way the well known class of vectorial matroids over a field.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Optimization Algorithms Research · Advanced Graph Theory Research