Skew-adjacency matrices of tournaments with bounded principal minors

被引：1

作者：

Boussairi, Abderrahim ^{[1
]}

Ezzahir, Sara ^{[1
]}

Lakhlifi, Soufiane ^{[1
]}

Mahzoum, Soukaina ^{[1
]}

机构：

[1] Hassan II Univ Casablanca, Fac Sci Ain Chock, Lab Math Fondamentales & Appl, Casablanca, Morocco

来源：

DISCRETE MATHEMATICS | 2023年 / 346卷 / 10期

关键词：

Tournament; Skew-adjacency matrix; Principal minor; Diamonds; Transitive blowup; ENERGY;

D O I：

10.1016/j.disc.2023.113552

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let T be a tournament with n vertices v1, ... , vn. The skew-adjacency matrix of T is the n x n zero-diagonal matrix S = [sij] in which sij = -sji =1 if vi dominates vj. It is well-known that the determinant of S is zero or the square of an odd integer. Moreover, the principal minors of S are at most 1 if and only if T is a local order. In this paper, we characterize the class of tournaments for which the principal minors of the skew-adjacency matrix do not exceed 9.& COPY; 2023 Elsevier B.V. All rights reserved.

引用

页数：6

共 50 条

[41] Correction: Extreme eigenvalues of principal minors of random matrices with moment conditions
Jianwei Hu
Seydou Keita
Kang Fu
Journal of the Korean Statistical Society, 2023, 52 : 765 - 765
[42] A CONSTRUCTIVE CHARACTERIZATION OF Q0-MATRICES WITH NONNEGATIVE PRINCIPAL MINORS
AGANAGIC, M
COTTLE, RW
MATHEMATICAL PROGRAMMING, 1987, 37 (02) : 223 - 231
[43] Characterization of product inequalities for principal minors of M-matrices and inverse M-matrices
Fallat, SM
Hall, HT
Johnson, CR
QUARTERLY JOURNAL OF MATHEMATICS, 1998, 49 (196): : 451 - 458
[44] Difference families, skew Hadamard matrices, and Critical groups of doubly-regular tournaments
Pantangi, Venkata Raghu Tej
ELECTRONIC JOURNAL OF COMBINATORICS, 2019, 26 (03):
[45] The computational complexity of three graph problems for instances with bounded minors of constraint matrices
Gribanov, D. V.
Malyshev, D. S.
DISCRETE APPLIED MATHEMATICS, 2017, 227 : 13 - 20
[46] The computational complexity of dominating set problems for instances with bounded minors of constraint matrices
Malyshev, D. S.
Gribanov, D., V
DISCRETE OPTIMIZATION, 2018, 29 : 103 - 110
[47] On Wilks' joint moment formulas for embedded principal minors of Wishart random matrices
Genest, C.
Ouimet, F.
Richards, D.
STAT, 2024, 13 (02):
[48] On the Gaussian product inequality conjecture for disjoint principal minors of Wishart random matrices
Genest, Christian
Ouimet, Frederic
Richards, Donald
ELECTRONIC JOURNAL OF PROBABILITY, 2024, 29 : 1 - 26
[49] Set-theoretic defining equations of the variety of principal minors of symmetric matrices
Oeding, Luke
ALGEBRA & NUMBER THEORY, 2011, 5 (01) : 75 - 109
[50] The enhanced principal rank characteristic sequence for skew-symmetric matrices
Fallat, Shaun M.
Olesky, Dale D.
van den Driessche, Pauline
LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 498 : 366 - 377

← 1 2 3 4 5 →