Symmetric alternating sign matrices

被引：0

作者：

Brualdi, Richard A. ^{[1
]}

Kim, Hwa Kyung ^{[2
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Sangmyung Univ, Dept Math Educ, Seoul 110743, South Korea

来源：

AUSTRALASIAN JOURNAL OF COMBINATORICS | 2014年 / 60卷

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we consider completions of n x n symmetric (0, -1)-matrices to symmetric alternating sign matrices by replacing certain 0s with + 1s. In particular, we prove that any n x n symmetric (0, -1)-matrix that can be completed to an alternating sign matrix by replacing some 0s with + 1s can be completed to a symmetric alternating sign matrix. Similarly, any n x n symmetric (0, + 1)-matrix that can be completed to an alternating sign matrix by replacing some 0s with -1s can be completed to a symmetric alternating sign matrix.

引用

页码：333 / 345

页数：13

共 50 条

[1] Alternating sign matrices and totally symmetric plane partitions
Fischer, Ilse
Schreier-Aigner, Florian
ALGEBRAIC COMBINATORICS, 2024, 7 (05):
[2] Diagonally and antidiagonally symmetric alternating sign matrices of odd order
Behrend, Roger E.
Fischer, Ilse
Konvalinka, Matjaz
ADVANCES IN MATHEMATICS, 2017, 315 : 324 - 365
[3] Vertically symmetric alternating sign matrices and a multivariate Laurent polynomial identity
Fischer, Ilse
Riegler, Lukas
ELECTRONIC JOURNAL OF COMBINATORICS, 2015, 22 (01):
[4] Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order
Ayyer, Arvind
Behrend, Roger E.
Fischer, Ilse
ADVANCES IN MATHEMATICS, 2020, 367
[5] Alternating Sign Matrices and Polynomiography
Kalantari, Bahman
ELECTRONIC JOURNAL OF COMBINATORICS, 2011, 18 (02):
[6] Completions of Alternating Sign Matrices
Richard A. Brualdi
Hwa Kyung Kim
Graphs and Combinatorics, 2015, 31 : 507 - 522
[7] Patterns of alternating sign matrices
Brualdi, Richard A.
Kiernan, Kathleen P.
Meyer, Seth A.
Schroeder, Michael W.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (10) : 3967 - 3990
[8] Alternating sign matrices and tournaments
Chapman, R
ADVANCES IN APPLIED MATHEMATICS, 2001, 27 (2-3) : 318 - 335
[9] ALTERNATING-SIGN MATRICES
BOUSQUETMELOU, M
HABSIEGER, L
DISCRETE MATHEMATICS, 1995, 139 (1-3) : 57 - 72
[10] DETERMINANTS AND ALTERNATING SIGN MATRICES
ROBBINS, DP
RUMSEY, H
ADVANCES IN MATHEMATICS, 1986, 62 (02) : 169 - 184

← 1 2 3 4 5 →