منابع مشابه
Total Characters and Chebyshev Polynomials
The total character τ of a finite group G is defined as the sum of all the irreducible characters of G. K. W. Johnson asks when it is possible to express τ as a polynomial with integer coefficients in a single irreducible character. In this paper, we give a complete answer to Johnson’s question for all finite dihedral groups. In particular, we show that, when such a polynomial exists, it is uni...
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We introduce quantized Chebyshev polynomials as deformations of generalized Chebyshev polynomials previously introduced by the author in the context of acyclic coefficient-free cluster algebras. We prove that these quantized polynomials arise in cluster algebras with principal coefficients associated to acyclic quivers of infinite representation types and equioriented Dynkin quivers of type A. ...
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Algebraic properties of Chebyshev polynomials are presented. The complete factorization of Chebyshev polynomials of the rst kind (Tn(x)) and second kind (Un(x)) over the integers are linked directly to divisors of n and n + 1 respectively. For any odd integer n, it is shown that the polynomial Tn(x)=x is irreducible over the integers i n is prime. The result leads to a generalization of Fermat'...
متن کاملSymmetrized Chebyshev Polynomials
We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves alternate) result that their coefficients are non-negative. As a corollary we find that Tn(c cos θ) and Un(c cos θ) are positive definite functions. We further s...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2003
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171203201046