Extremal matrices for the Bruhat-graph order

@article{Fernandes2020ExtremalMF,
  title={Extremal matrices for the Bruhat-graph order},
  author={Ros{\'a}rio Fernandes and Susana Borges Furtado},
  journal={Linear and Multilinear Algebra},
  year={2020},
  volume={69},
  pages={1255 - 1274}
}
We consider the class of symmetric -matrices with zero trace and constant row sums k which can be identified with the class of the adjacency matrices of k-regular undirected graphs. In a previous paper, two partial orders, the Bruhat and the Bruhat-graph order, have been introduced in this class. In fact, when k = 1 or k = 2, it was shown that the two orders coincide, while for the two orders are distinct. In this paper we give general properties of minimal and maximal matrices for these orders… 

On certain trees with the same degree sequence

On the little secondary Bruhat order

Let $R$ and $S$ be two sequences of positive integers in nonincreasing order having the same sum. We denote by ${\cal A}(R,S)$ the class of all $(0,1)$-matrices having row sum vector $R$ and column

The Bruhat order on classes of isotopic Latin squares

In a previous paper, the authors introduced and studied the Bruhat order in the class of Latin squares of order n. In this paper, we investigate the restriction of the Bruhat order in a class of

References

SHOWING 1-9 OF 9 REFERENCES

On the Bruhat order of labeled graphs

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

A BRUHAT ORDER FOR THE CLASS OF (0, 1)-MATRICES WITH ROW SUM VECTOR R AND COLUMN SUM VECTOR S ∗

Generalizing the Bruhat order for permutations (so for permutation matrices), a Bruhat order is defined for the class of m by n (0, 1)-matrices with a given row and column sum vector. An algorithm is

More on the Bruhat order for (0, 1)-matrices

Classes of (0, 1)-matrices Where the Bruhat Order and the Secondary Bruhat Order Coincide

TLDR
It is proved that if R = (2,2,…,2) orR = (1,1,….,1), then the Bruhat order and the Secondary Bruhat Order on \(\mathcal {A}(R,S)\) coincide.

Combinatorial Matrix Classes

1. Introduction 2. Basic existence theorems for matrices with prescribed properties 3. The class A(R S) of (0,1)-matrices 4. More on the class A(R S) of (0,1)-matrices 5. The class T(R) of tournament

THE GEOMETRY OF CONVEX CONES ASSOCIATED WITH THE LYAPUNOV INEQUALITY AND THE COMMON LYAPUNOV FUNCTION PROBLEM

In this paper, the structure of several convex cones that arise in the studyof Lyapunov functions is investigated. In particular, the cones associated with quadratic Lyapunov functions for both