منابع مشابه
Lamps, Factorizations, and Finite Fields
The origin of this study is the 1993 International Mathematical Olympiads, held at Istanbul, Turkey. Problem # 6, which occurred on day 2, reads: Let n > 1 be an integer. There are n lamps L0, . . . , Ln−1 arranged in a circle. Each lamp is either ON or OFF. A sequence of steps S0, S1, . . . , Sj , . . . is carried out. Step Sj affects the state of Lj only (leaving the state of all others lamps...
متن کاملExplicit Factorizations of Cyclotomic and Dickson Polynomials over Finite Fields
We give, over a finite field Fq, explicit factorizations into a product of irreducible polynomials, of the cyclotomic polynomials of order 3 · 2, the Dickson polynomials of the first kind of order 3 · 2 and the Dickson polynomials of the second kind of order 3 · 2 − 1.
متن کاملSome new perfect one-factorizations from starters in finite fields
We construct seven new examples of perfect one-factorizations, in the complete graphs K170, K730. K1370. K1850t and K3126. These are generated by twoand four-quotient starters in finite fields. We also find several examples of perfect one-factorizations that are not isomorphic to previously known examples.
متن کاملExplicit factorizations of cyclotomic polynomials over finite fields
In this paper, we make an attempt to study the explicit factorization of 2.7-th cyclotomic polynomials over finite field Fq when q ≡ 1(mod 4) into a product of distinct monic irreducible polynomials, where q is a power of an odd prime. AMS Subject Classification: 11T06, 11T22, 12Y05
متن کاملFinite Group Factorizations and Braiding
We compute the quantum double, braiding and other canonical Hopf algebra constructions for the bicrossproduct Hopf algebra H associated to the factorization of a finite group into two subgroups. The representations of the quantum double are described by a notion of bicrossed bimodules, generalising the cross modules of Whitehead. We also show that self-duality structures for the bicrossproduct ...
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 2000
ISSN: 0002-9890,1930-0972
DOI: 10.1080/00029890.2000.12005216