On the Dowling and Rhodes lattices and wreath products

• Tipo: Artigo em Revista Científica Internacional
• Data: 2021

Autores

Margolis, S (Autor) Outra; Rhodes, J (Autor) Outra; Pedro V. Silva (Autor) FCUP

Revista

Título: Journal of Algebra

Vol. 578

Páginas: 55-91

ISSN: 0021-8693

Editora: Elsevier

Indexação

ISI Web of Knowledge - 1 Citação

Scopus - 1 Citação

Outras Informações

ID Authenticus: P-00T-Q6Y

DOI: 10.1016/j.jalgebra.2021.02.018

Abstract (EN): Dowling and Rhodes defined different lattices on the set of triples (Subset, Partition, Cross Section) over a fixed finite group G. Although the Rhodes lattice is not a geometric lattice, it defines a matroid in the sense of the theory of boolean representable simplicial complexes. This turns out to be the direct sum of a uniform matroid with the lift matroid of the complete gain link graph over G. As is well known, the Dowling lattice defines the frame matroid over a similar gain graph. This gives a new perspective on both matroids and also an application of matroid theory to the theory of finite semigroups. We also make progress on an important question for these classical matroids: what are the minimal boolean representations and the minimum degree of a boolean matrix representation?

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 37