A unified approach to polynomial sequences with only real zeros

被引：115
作者：
Liu, Lily L. [1 ]
Wang, Yi [1 ]
机构：
[1] Dalian Univ Technol, Dept Appl Math, Dalian 116024, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS | 2007年 / 38卷 / 04期
基金：
美国国家科学基金会;
关键词：
polynomials withonly real zeros; polynomial sequences; recurrence relations;
D O I：
10.1016/j.aam.2006.02.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials, matching polynomials, Narayana polynomials and Eulerian polynomials. We also settle certain conjectures of Stahl on genus polynomials by proving them for certain classes of graphs, while showing that they are false in general. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：542 / 560
页数：19
相关论文
共 64 条
[1]  
[Anonymous], 1997, ENUMERATIVE COMBINAT
[2]  
[Anonymous], 1989, MEM AM MATH SOC
[3]   On Whitney numbers of Dowling lattices [J].
Benoumhani, M .
DISCRETE MATHEMATICS, 1996, 159 (1-3) :13-33
[4]   Log-concavity of Whitney numbers of Dowling lattices [J].
Benoumhani, M .
ADVANCES IN APPLIED MATHEMATICS, 1999, 22 (02) :186-189
[5]   On some numbers related to Whitney numbers of Dowling lattices [J].
Benoumhani, M .
ADVANCES IN APPLIED MATHEMATICS, 1997, 19 (01) :106-116
[6]  
Bjorner A., 2005, Graduate Texts in Mathematics, V231, DOI 10.1007/3-540-27596-7
[7]   Symmetry and unimodality in t-stack sortable permutations (vol 98, pg 201, 2002) [J].
Bóna, M .
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2002, 99 (01) :191-194
[8]  
Bona M., 2002, ELECTRON J COMB, V9, pA1
[9]   SOME Q-ANALOGS OF THE SCHRODER NUMBERS ARISING FROM COMBINATORIAL STATISTICS ON LATTICE PATHS [J].
BONIN, J ;
SHAPIRO, L ;
SIMION, R .
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1993, 34 (01) :35-55
[10]  
BRANDEN P, MATHCO0303149
1234567