منابع مشابه
Pythagorean powers of hypercubes
For n ∈ N consider the n-dimensional hypercube as equal to the vector space F2 , where F2 is the field of size two. Endow F2 with the Hamming metric, i.e., with the metric induced by the `1 norm when one identifies F2 with {0, 1} ⊆ R. Denote by `2 (F2 ) the n-fold Pythagorean product of F2 , i.e., the space of all x = (x1, . . . , xn) ∈ ∏n j=1 F n 2 , equipped with the metric ∀x, y ∈ n ∏ j=1 F2...
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We point out that the optimal pebbling number of the n-cube is (4 3) n+O(log n) , and explain how to approximate the optimal pebbling number of the nth cartesian power of any graph in a similar way. Let G be a graph. By a distribution of pebbles on G we mean a function a : V (G) ! Z 0 ; we usually write a(v) as a v , and call a v the number of pebbles on v. A pebbling move on a distribution cha...
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In this paper, we show that Q n is a divisor graph, for n = 2, 3. For n ≥ 4, we show that Q n is a divisor graph iff k ≥ n− 1. For folded-hypercube, we get FQn is a divisor graph when n is odd. But, if n ≥ 4 is even integer, then FQn is not a divisor graph. For n ≥ 5, we show that (FQn) k is not a divisor graph, where 2 ≤ k ≤ ⌈ 2 ⌉ − 1.
متن کاملPythagorean Triples
Let n be a number. We say that n is square if and only if: (Def. 3) There exists m such that n = m2. Let us note that every number which is square is also natural. Let n be a natural number. Note that n2 is square. Let us observe that there exists a natural number which is even and square. Let us observe that there exists a natural number which is odd and square. Let us mention that there exist...
متن کاملPythagorean Triples
The name comes from elementary geometry: if a right triangle has leg lengths x and y and hypotenuse length z, then x + y = z. Of course here x, y, z are positive real numbers. For most integer values of x and y, the integer x + y will not be a perfect square, so the positive real number √ x2 + y2 will be irrational: e.g. x = y = 1 =⇒ z = √ 2. However, a few integer solutions to x + y = z are fa...
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ژورنال
عنوان ژورنال: Annales de l'Institut Fourier
سال: 2016
ISSN: 1777-5310
DOI: 10.5802/aif.3032