Layered Restrictions and Chebyshev Polynomials
نویسندگان
چکیده
منابع مشابه
Layered Restrictions and Chebyshev
Abstract. A permutation is called layered if it consists of the disjoint union of substrings (layers) so that the entries decrease within each layer, and increase between the layers. We find the generating function for the number of permutations on n letters avoiding (1, 2, 3) and a layered permutation on k letters. In the most interesting case of two layers, the generating function depends onl...
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Abstract. A permutation is called layered if it consists of the disjoint union of substrings (layers) so that the entries decrease within each layer, and increase between the layers. We find the generating function for the number of permutations on n letters avoiding (1, 2, 3) and a layered permutation on k letters. In the most interesting case of two layers, the generating function depends onl...
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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'...
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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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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2001
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-001-8021-9