Minimal matrices in the Bruhat order for symmetric (0,1)-matrices

• Type: Article in International Scientific Journal
• Date: 2017

Authors

Susana Borges Furtado (Author) FEP; da Cruz, HF (Author) Other; Fernandes, R (Author) Other

Journal

Title: Linear Algebra and Its Applications

Vol. 530

Pages: 160-184

ISSN: 0024-3795

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 12 Citations

Scopus - 12 Citations

Other information

Authenticus ID: P-00M-TJA

DOI: 10.1016/j.laa.2017.05.014

Abstract (EN): In this paper we study the minimal matrices for the Bruhat order on the class of symmetric (0,1)-matrices with given row sum vector. We will show that, when restricted to the symmetric matrices, new minimal matrices may appear besides the symmetric matrices for the nonrestricted Bruhat order. We modify the algorithm presented by Brualdi and Hwang (2004), which gives a minimal matrix for the Bruhat order on the class of (0,1)-matrices with given row and column sum vectors, in order to obtain a minimal matrix for the Bruhat order on the class of symmetric (0,1)-matrices with given row sum vector. We identify other minimal matrices in some of these classes. Namely, we determine all the minimal matrices when the row sums are constant and equal to 3. We then describe a family of symmetric matrices that are minimal for the Bruhat order on the class of 2k-by-2k (0,1)-matrices with constant row sums equal to k+1 and identify, in terms of the term rank of a matrix, a class of symmetric matrices that are related in the Bruhat order with one of these minimal matrices. © 2017 Elsevier Inc.

Language: English

Type (Professor's evaluation): Scientific