Necklaces, Self-Reciprocal Polynomials, and q-Cycles
نویسندگان
چکیده
منابع مشابه
Self-reciprocal Polynomials Over Finite Fields
The reciprocal f ∗(x) of a polynomial f(x) of degree n is defined by f ∗(x) = xf(1/x). A polynomial is called self-reciprocal if it coincides with its reciprocal. The aim of this paper is threefold: first we want to call attention to the fact that the product of all self-reciprocal irreducible monic (srim) polynomials of a fixed degree has structural properties which are very similar to those o...
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Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an Ž . equivalence class of k-ary strings under rotation the cyclic group . A k-ary unlabeled necklace is an equivalence class of k-ary strings under rotation and permutation of alphabet symbols. We present new, fast, simple, recursive algoŽ . rit...
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The main result of this paper is a sharp integral mean inequality for the derivative of a ‘self-reciprocal’ polynomial.
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Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to aself reciprocal polynomials defined in [4]. We consider the properties for the divisibility of a-reciprocal polynomials, estimate the number of all nontrivial a-self reciprocal irreducible monic polynomials and characterize the parity of the number of irreducible f...
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Let q be a power of an odd prime and let k, n ∈ N such that 1 < k ≤ n. We investigate the existence of self-reciprocal irreducible monic polynomials over Fq, of degree 2n and their k-th coefficient prescribed.
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ژورنال
عنوان ژورنال: International Journal of Combinatorics
سال: 2014
ISSN: 1687-9163,1687-9171
DOI: 10.1155/2014/593749