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

^*此作品的通信作者

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研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

摘要

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.

原文	英語
頁（從 - 到）	209-223
頁數	15
期刊	Linear Algebra and Its Applications
卷	457
DOIs	https://doi.org/10.1016/j.laa.2014.05.027
出版狀態	已發佈 - 2014 9月 15

ASJC Scopus subject areas

代數與數理論
數值分析
幾何和拓撲
離散數學和組合

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10.1016/j.laa.2014.05.027

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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). ",

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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

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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

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ASJC Scopus subject areas

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