منابع مشابه
On Regular Polytope Numbers
Lagrange proved a theorem which states that every nonnegative integer can be written as a sum of four squares. This result can be generalized in two directions. The one is a horizontal generalization which is known as polygonal number theorem, and the other is a higher dimensional generalization which is known as Hilber-Waring problem. In this paper, we shall generalize Lagrange’s sum of four s...
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In order to be able to draw inferences about real world phenomena from a representation expressed in a digital computer, it is essential that the representation should have a rigorously correct algebraic structure. It is also desirable that the underlying algebra be familiar, and provide a close modelling of those phenomena. The fundamental problem addressed in this paper is that, since compute...
متن کاملAN EXTREMUM PROPERTY CHARACTERIZING THE n-DIMENSIONAL REGULAR CROSS-POLYTOPE
In the spirit of the Genetics of the Regular Figures, by L. Fejes Tóth [FT, Part 2], we prove the following theorem: If 2n points are selected in the n-dimensional Euclidean ball Bn so that the smallest distance between any two of them is as large as possible, then the points are the vertices of an inscribed regular cross-polytope. This generalizes a result of R.A. Rankin [R] for 2n points on t...
متن کاملOn the transcendence of real numbers with a regular expansion
We apply the Ferenczi–Mauduit combinatorial condition obtained via a reformulation of Ridout’s theorem to prove that a real number whose b-ary expansion is the coding of an irrational rotation on the circle with respect to a partition in two intervals is transcendental. We also prove the transcendence of real numbers whose b-ary expansion arises from a nonperiodic three-interval exchange transf...
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This note resolves an open problem asked by Bezrukov in the open problem session of IWOCA 2014. It shows an equivalence between regular graphs and graphs for which a sequence of invariants presents some symmetric property. We extend this result to a few other sequences.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06710-2