منابع مشابه
Nathanson heights in finite vector spaces
Let p be a prime, and let Zp denote the field of integers modulo p. The Nathanson height of a point v ∈ Z p is the sum of the least nonnegative integer representatives of its coordinates. The Nathanson height of a subspace V ⊆ Z p is the least Nathanson height of any of its nonzero points. In this paper, we resolve a conjecture of Nathanson [M. B. Nathanson, Heights on the finite projective lin...
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In this paper, we extend the definition of the Nathanson height from points in projective spaces over Fp to points in projective spaces over arbitrary finite fields. If [a0 : . . . : an] ∈ P(Fp), then the Nathanson height is hp([a0 : a1 : . . . : ad]) = min b∈Fp d ∑ i=0 H(bai) where H(ai) = |N(ai)|+p(deg(ai)−1) with N the field norm and |N(ai)| the element of {0, 1, . . . , p− 1} congruent to N...
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For a finite vector space V and a non-negative integer r ≤ dim V we estimate the smallest possible size of a subset of V , containing a translate of every rdimensional subspace. In particular, we show that if K ⊆ V is the smallest subset with this property, n denotes the dimension of V , and q is the size of the underlying field, then for r bounded and r < n ≤ rq we have |V \K| = Θ(nq); this im...
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Example 3. If X ⊆ RN is a vector space then it is a vector subspace of RN . Example 4. R1 is a vector subspace of R2. But the set [−1, 1] is not a vector subspace because it is not closed under either vector addition or scalar multiplication (for example, 1 + 1 = 2 6∈ [−1, 1]). Geometrically, a vector space in RN looks like a line, plane, or higher dimensional analog thereof, through the origin...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2008
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2008.03.004