Results 21 to 30 of about 713,237 (306)
Some extensions for the several combinatorial identities
Advances in Difference Equations, 2021 In this paper, we give some extensions for Mortenson’s identities in series with the Bell polynomial using the partial fraction decomposition. As applications, we obtain some combinatorial identities involving the harmonic numbers.
Gao-Wen Xi, Qiu-Ming Luo
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Symmetric Identities for Euler Polynomials [PDF]
Graphs and Combinatorics, 2010 9 pages. Accepted by Graphs and Combinatorics.
Yong Zhang, Zhi-Wei Sun, Hao Pan
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Matrix Approaches for Gould–Hopper–Laguerre–Sheffer Matrix Polynomial Identities
Axioms, 2023 The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational methods, but in this paper, we investigate them using matrix techniques.
Tabinda Nahid +2 more
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The Abel-Type Polynomial Identities [PDF]
The Electronic Journal of Combinatorics, 2010 The Abel identity is $(x+y)^{n}=\sum\limits_{i=0}^{n}{n\choose i}x (x-iz)^{i-1}(y+iz)^{n-i}$, where $x,y$ and $z$ are real numbers. In this paper we deduce several polynomials expansions, referred to as Abel-type identities, by using Foata's method, and also show some of their applications.
Fengying Huang, Bolian Liu
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Some symmetric polynomial and related identities [PDF]
ریاضی و جامعهIn this paper, we study some symmetric polynomials and their properties. In addition to the elementary and complete symmetric polynomials, we consider the accumulative versions of these polynomials and using common combinatorial tools, particularly ...
Narges Ghareghani +1 more
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CC-circuits and the expressive power of nilpotent algebras [PDF]
Logical Methods in Computer Science, 2022 We show that CC-circuits of bounded depth have the same expressive power as circuits over finite nilpotent algebras from congruence modular varieties. We use this result to phrase and discuss a new algebraic version of Barrington, Straubing and Th\'erien'
Michael Kompatscher
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Identity-Type Functions and Polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 For a noncommuting product of functions, similar to convolutions, an “identity-type function” leaving a specific function invariant is defined. It is evaluated for any choice of function on which it acts by solving a functional equation. A closed-form representation for the identity-type function of(1+t)−b(b>0)is obtained, which is a solution of a ...
M. Aslam Chaudhry, Asghar Qadir
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Identities on factorial Grothendieck polynomials [PDF]
Advances in Applied Mathematics, 2019 Gustafson and Milne proved an identity on the Schur function indexed by a partition of the form $(λ_1-n+k,λ_2-n+k,\ldots,λ_k-n+k)$. On the other hand, Fehér, Némethi and Rimányi found an identity on the Schur function indexed by a partition of the form $(m-k,\ldots,m-k, λ_1,\ldots,λ_k)$.
Peter L. Guo, Sophie C. C. Sun
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The Polarization Theorem and Polynomial Identities for Matrix Functions
Известия Иркутского государственного университета: Серия "Математика", 2017 In this article the simple combinatorial proof of the known polarization theorem (about the restoration of a polyadditive symmetric function over its values on a diagonal) is given.
G.P. Egorychev
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Polynomial identities on eigenforms
Journal of Number Theory, 2016 In this paper, we fix a polynomial with complex coefficients and determine the eigenforms for SL2(Z) which can be expressed as the fixed polynomial evaluated at other eigenforms. In particular, we show that when one excludes trivial cases, only finitely many such identities hold for a fixed polynomial.
Richey, Joseph, Shutty, Noah
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