On the Dowling and Rhodes lattices and wreath products

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Margolis, S (Author) Other; Rhodes, J (Author) Other; Pedro V. Silva (Author) FCUP

Journal

Title: Journal of Algebra

Vol. 578

Pages: 55-91

ISSN: 0021-8693

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: 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?

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 37