A GENERALIZED NEWTON-GIRARD FORMULA FOR MONOMIAL SYMMETRIC POLYNOMIALS

被引：6
|
作者：
Chamberlin, Samuel [1 ]
Rafizadeh, Azadeh [2 ]
机构：
[1] Park Univ, Dept Math & Stat, Parkville, MO 64152 USA
[2] William Jewell Coll, Dept Math & Data Sci, Liberty, MO USA
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2020年 / 50卷 / 03期
关键词：
symmetric polynomials; Newton-Girard formula;
D O I：
10.1216/rmj.2020.50.941
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Newton-Girard Formula allows one to write any elementary symmetric polynomial as a sum of products of power sum symmetric polynomials and elementary symmetric polynomials of lesser degree. It has numerous applications. We have generalized this identity by replacing the elementary symmetric polynomials with monomial symmetric polynomials. Our formula has an application in the field of Lie algebras.
引用
收藏
页码：941 / 946
页数：6
相关论文
共 50 条
  • [1] Generalized Power Sum and Newton-Girard Identities
    Sudip Bera
    Sajal Kumar Mukherjee
    [J]. Graphs and Combinatorics, 2020, 36 : 1957 - 1964
  • [2] Generalized Power Sum and Newton-Girard Identities
    Bera, Sudip
    Mukherjee, Sajal Kumar
    [J]. GRAPHS AND COMBINATORICS, 2020, 36 (06) : 1957 - 1964
  • [3] On the MacMahon generalization of the Newton-Girard formulae
    Gegenbauer, L
    [J]. PROCEEDINGS OF THE KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, 1901, 3 : 347 - 351
  • [4] Combinatorial proofs of the Newton-Girard and Chapman-Costas-Santos identities
    Mukherjee, Sajal Kumar
    Bera, Sudip
    [J]. DISCRETE MATHEMATICS, 2019, 342 (06) : 1577 - 1580
  • [5] Generalized Newton complementary duals of monomial ideals
    Ansaldi, Katie
    Lin, Kuei-Nuan
    Shen, Yi-Huang
    [J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2021, 20 (02)
  • [6] Newton polytope of good symmetric polynomials
    Duc-Khanh Nguyen
    Nguyen Thi Ngoc Giao
    Dang Tuan Hiep
    Do Le Hai Thuy
    [J]. COMPTES RENDUS MATHEMATIQUE, 2023, 361 (01) : 767 - 775
  • [7] Newton polytopes and symmetric Grothendieck polynomials
    Escobar, Laura
    Yong, Alexander
    [J]. COMPTES RENDUS MATHEMATIQUE, 2017, 355 (08) : 831 - 834
  • [8] Analogues of Newton-Girard power-sum formulas for entire and meromorphic functions with applications to the Riemann zeta function
    Bagdasaryan, Armen
    Araci, Serkan
    Acikgoz, Mehmet
    Srivastava, H. M.
    [J]. JOURNAL OF NUMBER THEORY, 2015, 147 : 92 - 102
  • [9] Special Case of the Generalized Girard-Waring Formula
    Merca, Mircea
    [J]. JOURNAL OF INTEGER SEQUENCES, 2012, 15 (05)
  • [10] An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials
    Xu, Y
    [J]. ADVANCES IN APPLIED MATHEMATICS, 2002, 29 (02) : 328 - 343
12345