Polynomials satisfying a binomial theorem
نویسندگان
چکیده
منابع مشابه
A Digital Binomial Theorem
In this article, we demonstrate how the Binomial Theorem in turn arises from a one-parameter generalization of the Sierpinski triangle. The connection between them is given by the sum-of-digits function, s(k), defined as the sum of the digits in the binary representation of k (see [1]). For example, s(3) = s(1·2+1·2) = 2. Towards this end, we begin with a well-known matrix formulation of Sierpi...
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For a prime power q, let Fq be the finite field with q elements and F ∗ q denote its multiplicative group. A polynomial f ∈ Fq[x] is called a permutation polynomial (PP) if its associated polynomial mapping f : c 7→ f(c) from Fq to itself is a bijection. A permutation polynomial f(x) is referred to as a complete permutation polynomial (CPP) if f(x)+x is also a permutation over Fq [4]. Permutati...
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A loop satisfies Moufang’s theorem whenever the subloop generated by three associating elements is a group. Moufang loops (loops that satisfy the Moufang identities) satisfy Moufang’s theorem, but it is possible for a loop that is not Moufang to nevertheless satisfy Moufang’s theorem. Steiner loops that are not Moufang loops are known to arise from Steiner triple systems in which some triangle ...
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متن کاملA Generalization of the Digital Binomial Theorem
In [9], the author introduced a digital version of this theorem where the exponents appearing in (1) are viewed as sums of digits. To illustrate this, consider the binomial theorem for N = 2: (x + y) = xy + xy + xy + xy. (2) It is easy to verify that (2) is equivalent to (x+ y) = xy + xy + xy + xy, (3) where s(k) denotes the sum of digits of k expressed in binary. For example, s(3) = s(1 · 2 + ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1970
ISSN: 0022-247X
DOI: 10.1016/0022-247x(70)90276-3