Variances and determinantal profiles of orientations

Huilan Chang; Sen Peng Eu; Pei Lan Yen

doi:10.1016/j.laa.2014.05.027

Variances and determinantal profiles of orientations

Huilan Chang^*, Sen Peng Eu, Pei Lan Yen

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Given a simple graph G, let X be the random variable which is the determinant of the (oriented) adjacency matrix of an orientation of G. It is known that the expectation E(X) equals the number of perfect matchings of G. In this paper we give a graphical interpretation of the variance Var(X). We also give complete determinantal profiles of several classes of graphs, including wheels, fans, and general books.

Original language	English
Pages (from-to)	209-223
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	457
DOIs	https://doi.org/10.1016/j.laa.2014.05.027
Publication status	Published - 2014 Sept 15

Keywords

Determinant
Orientation
Pfaffian
Variance

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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title = "Variances and determinantal profiles of orientations",

abstract = "Given a simple graph G, let X be the random variable which is the determinant of the (oriented) adjacency matrix of an orientation of G. It is known that the expectation E(X) equals the number of perfect matchings of G. In this paper we give a graphical interpretation of the variance Var(X). We also give complete determinantal profiles of several classes of graphs, including wheels, fans, and general books.",

keywords = "Determinant, Orientation, Pfaffian, Variance",

author = "Huilan Chang and Eu, {Sen Peng} and Yen, {Pei Lan}",

note = "Funding Information: Research partially supported by NSC grants 100-2115-M-390-004-MY2 (H. Chang), 101-2115-M-390-004-MY3 (S.-P. Eu), NSC 100-2811-M-390-007 (P.-L. Yen). ",

year = "2014",

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language = "English",

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journal = "Linear Algebra and Its Applications",

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TY - JOUR

T1 - Variances and determinantal profiles of orientations

AU - Chang, Huilan

AU - Eu, Sen Peng

AU - Yen, Pei Lan

N1 - Funding Information: Research partially supported by NSC grants 100-2115-M-390-004-MY2 (H. Chang), 101-2115-M-390-004-MY3 (S.-P. Eu), NSC 100-2811-M-390-007 (P.-L. Yen).

PY - 2014/9/15

Y1 - 2014/9/15

N2 - Given a simple graph G, let X be the random variable which is the determinant of the (oriented) adjacency matrix of an orientation of G. It is known that the expectation E(X) equals the number of perfect matchings of G. In this paper we give a graphical interpretation of the variance Var(X). We also give complete determinantal profiles of several classes of graphs, including wheels, fans, and general books.

AB - Given a simple graph G, let X be the random variable which is the determinant of the (oriented) adjacency matrix of an orientation of G. It is known that the expectation E(X) equals the number of perfect matchings of G. In this paper we give a graphical interpretation of the variance Var(X). We also give complete determinantal profiles of several classes of graphs, including wheels, fans, and general books.

KW - Determinant

KW - Orientation

KW - Pfaffian

KW - Variance

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DO - 10.1016/j.laa.2014.05.027

M3 - Article

AN - SCOPUS:84901976328

SN - 0024-3795

VL - 457

SP - 209

EP - 223

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Variances and determinantal profiles of orientations

Abstract

Keywords

ASJC Scopus subject areas

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