On the little secondary bruhat order

Rosário Fernandes, Henrique F. Da Cruz, Domingos Salomão

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1 Citation (Scopus)

Abstract

Let R and S be two sequences of positive integers in nonincreasing order having the same sum. We denote by A(R, S) the class of all (0, 1)-matrices having row sum vector R and column sum vector S. Brualdi and Deaett (More on the Bruhat order for (0, 1)-matrices, Linear Algebra Appl., 421:219{232, 2007) suggested the study of the secondary Bruhat order on A(R, S) but with some constraints. In this paper, we study the cover relation and the minimal elements for this partial order relation, which we call the little secondary Bruhat order, on certain classes A(R, S). Moreover, we show that this order is different from the Bruhat order and the secondary Bruhat order. We also study a variant of this order on certain classes of symmetric matrices of A(R, S).

Original languageEnglish
Pages (from-to)113-126
Number of pages14
JournalElectronic Journal Of Linear Algebra
Volume37
DOIs
Publication statusPublished - Jan 2021

Keywords

  • (0, 1)-Matrices
  • Interchanges
  • Minimal elements
  • Secondary bruhat order

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