Characteristic polynomials of a permutation representation
نویسندگان
چکیده
منابع مشابه
A general representation theory for constructing groups of permutation polynomials
Using the left regular action of a group on itself, we develop a general representation theory for constructing groups of permutation polynomials. As an application of the method, we compute polynomial representations of several abelian and nonabelian groups, and we determine the equivalence classes of the groups of polynomials we construct. In particular, when the size of the group is equal to...
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Introduction. Let F be a field and let V be a finite dimensional vector space over F which is also a module over the ring F[a]. Here a may lie in any extension ring of F. We do not assume, as yet, that V is a faithful module, so that a need not be a linear transformation on V. It is known that by means of a decomposition of V into cyclic F[a]-modules we may obtain a definition of the characteri...
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This paper mainly studies problems about so called “permutation polynomials modulo m”, polynomials with integer coefficients that can induce bijections over Zm = {0, · · · , m−1}. The necessary and sufficient conditions of permutation polynomials are given, and the number of all permutation polynomials of given degree and the number induced bijections are estimated. A method is proposed to dete...
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We give an explicit formula of the inverse polynomial of a permutation polynomial of the form xrf(xs) over a finite field Fq where s | q − 1. This generalizes results in [6] where s = 1 or f = g q−1 s were considered respectively. We also apply our result to several interesting classes of permutation polynomials.
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We give an exact characterization of permutation polynomials mod ulo n w w a polynomial P x a a x adx d with integral coe cients is a permutation polynomial modulo n if and only if a is odd a a a is even and a a a is even We also characterize polynomials de ning latin squares mod ulo n w but prove that polynomial multipermutations that is a pair of polynomials de ning a pair of orthogonal latin...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1979
ISSN: 0097-3165
DOI: 10.1016/0097-3165(79)90054-2