Root geometry of polynomial sequences I: Type (0, 1)

Jonathan L. Gross; Toufik Mansour; Thomas W. Tucker; David G.L. Wang

doi:10.1016/j.jmaa.2015.08.039

Root geometry of polynomial sequences I: Type (0, 1)

Jonathan L. Gross, Toufik Mansour, Thomas W. Tucker, David G.L. Wang^*

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

This paper concerns the distribution in the complex plane of the roots of a polynomial sequence {Wn(x)}n≥0 given by a recursion W_n(x)=aW_n-1(x)+(bx+c)W_n-2(x), with W₀(x)=1 and W₁(x)=t(x-r), where a>0, b>0, and c, t, r∈R. Our results include proof of the distinct-real-rootedness of every such polynomial W_n(x), derivation of the best bound for the zero-set {x|W_n(x)=0for some n≥1}, and determination of three precise limit points of this zero-set. Also, we give several applications from combinatorics and topological graph theory.

源语言	英语
文章编号	19736
页（从-至）	1261-1289
页数	29
期刊	Journal of Mathematical Analysis and Applications
卷	433
期	2
DOI	https://doi.org/10.1016/j.jmaa.2015.08.039
出版状态	已出版 - 15 1月 2016

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10.1016/j.jmaa.2015.08.039

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引用此

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title = "Root geometry of polynomial sequences I: Type (0, 1)",

abstract = "This paper concerns the distribution in the complex plane of the roots of a polynomial sequence {Wn(x)}n≥0 given by a recursion Wn(x)=aWn-1(x)+(bx+c)Wn-2(x), with W0(x)=1 and W1(x)=t(x-r), where a>0, b>0, and c, t, r∈R. Our results include proof of the distinct-real-rootedness of every such polynomial Wn(x), derivation of the best bound for the zero-set {x|Wn(x)=0for some n≥1}, and determination of three precise limit points of this zero-set. Also, we give several applications from combinatorics and topological graph theory.",

keywords = "Genus distribution, Real-rooted polynomial, Recurrence, Root geometry",

author = "Gross, {Jonathan L.} and Toufik Mansour and Tucker, {Thomas W.} and Wang, {David G.L.}",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2016",

month = jan,

day = "15",

doi = "10.1016/j.jmaa.2015.08.039",

language = "English",

volume = "433",

pages = "1261--1289",

journal = "Journal of Mathematical Analysis and Applications",

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TY - JOUR

T1 - Root geometry of polynomial sequences I

T2 - Type (0, 1)

AU - Gross, Jonathan L.

AU - Mansour, Toufik

AU - Tucker, Thomas W.

AU - Wang, David G.L.

PY - 2016/1/15

Y1 - 2016/1/15

N2 - This paper concerns the distribution in the complex plane of the roots of a polynomial sequence {Wn(x)}n≥0 given by a recursion Wn(x)=aWn-1(x)+(bx+c)Wn-2(x), with W0(x)=1 and W1(x)=t(x-r), where a>0, b>0, and c, t, r∈R. Our results include proof of the distinct-real-rootedness of every such polynomial Wn(x), derivation of the best bound for the zero-set {x|Wn(x)=0for some n≥1}, and determination of three precise limit points of this zero-set. Also, we give several applications from combinatorics and topological graph theory.

AB - This paper concerns the distribution in the complex plane of the roots of a polynomial sequence {Wn(x)}n≥0 given by a recursion Wn(x)=aWn-1(x)+(bx+c)Wn-2(x), with W0(x)=1 and W1(x)=t(x-r), where a>0, b>0, and c, t, r∈R. Our results include proof of the distinct-real-rootedness of every such polynomial Wn(x), derivation of the best bound for the zero-set {x|Wn(x)=0for some n≥1}, and determination of three precise limit points of this zero-set. Also, we give several applications from combinatorics and topological graph theory.

KW - Genus distribution

KW - Real-rooted polynomial

KW - Recurrence

KW - Root geometry

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U2 - 10.1016/j.jmaa.2015.08.039

DO - 10.1016/j.jmaa.2015.08.039

M3 - Article

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SN - 0022-247X

VL - 433

SP - 1261

EP - 1289

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 19736

ER -

Root geometry of polynomial sequences I: Type (0, 1)

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