Zhongshan Li

activity

20122017

most citedMinimum ranks of sign patterns via sign vectors and duality

3 citations · 4 across the 7 of their papers we have counts for

collaborators

8 papers

math.CO2017

Sign patterns that require $H_{n}$ exist for each $n \geq 4$

Wei Gao, Zhongshan Li, Lihua Zhang

The refined inertia of a square real matrix $A$ is the ordered $4$ -tuple $(n_{+}, n_{-}, n_{z}, 2 n_{p})$ , where $n_{+}$ (resp., $n_{-}$ ) is the number of eigenvalues of $A$ with positive (resp…

math.CO2017

On the number of vertices of the stochastic tensor polytope

Zhongshan Li, Fuzhen Zhang, Xiao-Dong Zhang

This paper is devoted to the study of lower and upper bounds for the number of vertices of the polytope of $n \times n \times n$ stochastic tensors (i.e., triply stochastic arrays of…

math.CO2014

Two-connected signed graphs with maximum nullity at most two

Marina Arav, Frank J. Hall, Zhongshan Li +1

A signed graph is a pair $(G, Σ)$ , where $G = (V, E)$ is a graph (in which parallel edges are permitted, but loops are not) with $V = {1, \dots, n}$ and $Σ \subseteq E$ . The edges in $Σ$ …

math.CO2013

Sign patterns with minimum rank 3 and point-line configurations

Guangming Jing, Wei Gao, Yubin Gao +4

A \emph{sign pattern (matrix)} is a matrix whose entries are from the set ${+, -, 0}$ . The \emph{minimum rank} (respectively, \emph{rational minimum rank}) of a sign pattern matr…

math.CO2013★ 3 cited

Minimum ranks of sign patterns via sign vectors and duality

Marina Arav, Frank J. Hall, Zhongshan Li +3

A {\it sign pattern matrix} is a matrix whose entries are from the set ${+, -, 0}$ . The minimum rank of a sign pattern matrix $A$ is the minimum of the ranks of the real matrices…

math.CO2013

The minimum rank of a sign pattern matrix with a 1-separation

Marina Arav, Frank J. Hall, Zhongshan Li +3

A sign pattern matrix is a matrix whose entries are from the set ${+, -, 0}$ . If $A$ is an $m \times n$ sign pattern matrix, the qualitative class of $A$ , denoted $Q (A)$ , is the set…

math.CO2012

A graph minors characterization of signed graphs whose signed Colin de Verdière parameter $ν$ is two

Marina Arav, Frank J. Hall, Zhongshan Li +1

A signed graph is a pair $(G, Σ)$ , where $G = (V, E)$ is a graph (in which parallel edges are permitted, but loops are not) with $V = {1, ..., n}$ and $Σ \subseteq E$ . The edges in $Σ$ ar…

math.CO2012★ 1 cited

The inertia set of a signed graph

Marina Arav, Frank J. Hall, Zhongshan Li +1

A signed graph is a pair $(G, Σ)$ , where $G = (V, E)$ is a graph (in which parallel edges are permitted, but loops are not) with $V = 1, ..., n$ and $Σ \subseteq E$ . By $S (G, Σ)$ we denote…

Sign patterns that require Hn​ exist for each n≥4

On the number of vertices of the stochastic tensor polytope

Two-connected signed graphs with maximum nullity at most two

Sign patterns with minimum rank 3 and point-line configurations

Minimum ranks of sign patterns via sign vectors and duality

The minimum rank of a sign pattern matrix with a 1-separation

A graph minors characterization of signed graphs whose signed Colin de Verdière parameter ν is two

The inertia set of a signed graph

Sign patterns that require $H_{n}$ exist for each $n \geq 4$

A graph minors characterization of signed graphs whose signed Colin de Verdière parameter $ν$ is two