Symplectic Groups and Permutation Polynomials, Part II
نویسندگان
چکیده
منابع مشابه
Symplectic Spreads and Permutation Polynomials
Every symplectic spread of PG(3, q), or equivalently every ovoid of Q(4, q), is shown to give a certain family of permutation polynomials of GF (q) and conversely. This leads to an algebraic proof of the existence of the Tits-Lüneburg spread of W (2) and the Ree-Tits spread of W (3), as well as to a new family of low-degree permutation polynomials over GF (3). Let PG(3, q) denote the projective...
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Given a set S with n elements, consider all the possible one-to-one and onto functions from S to itself. This collection of functions is called the permutation group of S, because the functions are simply permuting the elements of S. We notice immediately that it doesn’t matter what the elements of S are (numbers, planets, tacos, etc) just that there are n distinct ones in the set, so we may re...
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In this paper we study, given a group G of permutations of a finite set, the so-called fixed point polynomial ∑n i=0 fix i, where fi is the number of permutations in G which have exactly i fixed points. In particular, we investigate how root location relates to properties of the permutation group. We show that for a large family of such groups most roots are close to the unit circle and roughly...
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The purpose of the present paper is to offer a very elementary approach to symplectic polynomials. Orthogonality it a very special characteristic, among other proprieties of this new type of polynomials.
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In a previous paper with the same title [1], I considered the following situation; G is a primitive, not doubly transitive permutation group on Q, in which the stabiliser G a of a point a acts doubly transitively on an orbit F(a), where |F(a)| = v. Manning [3] showed that, if v > 2, then G a has an orbit larger than F(a). Indeed, with A = F* o T (see [1] for notation), it is easy to see that A(...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2002
ISSN: 1071-5797
DOI: 10.1006/ffta.2001.0338