منابع مشابه
Heights on the Finite Projective Line
Define the height function h(a) = min{k + (ka mod p) : k = 1, 2, . . . , p − 1} for a ∈ {0, 1, . . . , p − 1.} It is proved that the height has peaks at p, (p+1)/2, and (p+c)/3, that these peaks occur at a = [p/3], (p−3)/2, (p− 1)/2, [2p/3], p − 3, p− 2, and p − 1, and that h(a) ≤ p/3 for all other values of a. 1. Heights on finite projective spaces Let p be an odd prime and let Fp = Z/pZ and F...
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We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes. We present sharp results on the size of the minimum percolating sets and the maximal non-percolating sets. Additional results on the minimal and maximal percolation time as well as on the critical probability in the projective plane are also presented.
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Let Fp = Z/pZ. The height of a point a = (a1, . . . , ad) ∈ F d p is hp(a) = min n Pd i=1(kai mod p) : k = 1, . . . , p − 1 o . Explicit formulas and estimates are obtained for the values of the height function in the case d = 2, and these results are applied to the problem of determining the minimum number of edges the must be deleted from a finite directed graph so that the resulting subgraph...
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If α1, . . . , αr are algebraic numbers such that N = r ∑
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In this paper we will suggest a construction for height functions for line bundles on arithmetic varieties. Following the philosophy of [BoGS] heights should be objects in arithmetic geometry analogous to degrees in algebraic geometry. So let K be a number field, OK its ring of integers and X /OK an arithmetic variety, i.e. a regular scheme, projective and flat over OK , whose generic fiber X/K...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2009
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s179304210900192x