DOAJ Open Access 2020

Relaxations of the matroid axioms I: Independence, Exchange and Circuits

Jose ́ Alejandro Samper

Lihat Sumber DOI

Abstrak

Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial complexes. The resulting classes retain some of the matroid properties and allow us to classify matroid properties according to the relevant axioms needed to prove them. We illustrate this by discussing Tutte polynomials. Furthermore, we extend a conjecture of Stanley on h-vectors and provide evidence to show that the extension is better suited than matroids to study the conjecture.

Topik & Kata Kunci

Mathematics

Penulis (1)

Jose ́ Alejandro Samper

Format Sitasi

APA MLA BibTeX

Samper, J.́.A. (2020). Relaxations of the matroid axioms I: Independence, Exchange and Circuits. https://doi.org/10.46298/dmtcs.6365

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6365

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6365
Akses: Open Access ✓