Combinatorially composing Chebyshev polynomials

被引：4
|
作者：
Benjamin, Arthur T. [1 ]
Walton, Daniel [2 ]
机构：
[1] Harvey Mudd Coll, Dept Math, Claremont, CA 91711 USA
[2] Univ Calif Los Angeles, Dept Atmospher & Ocean Sci, Los Angeles, CA 90095 USA
来源：
JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2010年 / 140卷 / 08期
关键词：
Chebyshev polynomials; Combinatorial proof; Tiling;
D O I：
10.1016/j.jspi.2010.01.012
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We present a combinatorial proof of two fundamental composition identities associated with Chebyshev polynomials. Namely, for all m, n >= 0, T(m)(T(n)(x)) = T(mn)(x) and U(m-1) (T(n)(x))U(n-1)(x) = U(mn-1)(x). (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：2161 / 2167
页数：7
相关论文
共 50 条
  • [31] Cryptosystem based on chebyshev polynomials
    Chen, Xiao-Song
    Sun, Yi-Wei
    Tiedao Xuebao/Journal of the China Railway Society, 2013, 35 (01): : 77 - 79
  • [32] Chebyshev Polynomials on Compact Sets
    Totik, Vilmos
    POTENTIAL ANALYSIS, 2014, 40 (04) : 511 - 524
  • [33] Discrete Entropies of Chebyshev Polynomials
    Sfetcu, Razvan-Cornel
    Sfetcu, Sorina-Cezarina
    Preda, Vasile
    MATHEMATICS, 2024, 12 (07)
  • [34] Chebyshev Polynomials on Compact Sets
    Vilmos Totik
    Potential Analysis, 2014, 40 : 511 - 524
  • [35] Optimization via Chebyshev polynomials
    Kareem T. Elgindy
    Journal of Applied Mathematics and Computing, 2018, 56 : 317 - 349
  • [36] Embedding Distributions and Chebyshev Polynomials
    Yichao Chen
    Toufik Mansour
    Qian Zou
    Graphs and Combinatorics, 2012, 28 : 597 - 614
  • [37] Gaussian quadrature of Chebyshev polynomials
    Hunter, DB
    Nikolov, G
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1998, 94 (02) : 123 - 131
  • [38] A combinatorial interpretation of the Chebyshev polynomials
    Munarini, Emanuele
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2006, 20 (03) : 649 - 655
  • [39] Fejer Sums and Chebyshev Polynomials
    Bustamante, Jorge
    Jesus Merino-Garcia, Juan
    Maria Quesada, Jose
    RESULTS IN MATHEMATICS, 2019, 74 (04)
  • [40] Chebyshev polynomials and Galois groups of De Moivre polynomials
    Girstmair, Kurt
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2022, 18 (08) : 1735 - 1748
12345