MSS sequences, colorings of necklaces, and periodic points of f(z) = z2 − 2
نویسندگان
چکیده
منابع مشابه
Integer Sequences and Periodic Points
Arithmetic properties of integer sequences counting periodic points are studied, and applied to the case of linear recurrence sequences, Bernoulli numerators, and Bernoulli denominators.
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A (continuous) necklace is simply an interval of the real line colored measurably with some number of colors. A well-known application of the Borsuk-Ulam theorem asserts that every k-colored necklace can be fairly split by at most k cuts (from the resulting pieces one can form two collections, each capturing the same measure of every color). Here we prove that for every k ≥ 1 there is a measura...
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In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and the icosahedral graph.
متن کاملPoints, Copoints, and Colorings
In 1935, Paul Erdős and George Szekeres were able to show that any point set large enough contains the vertices of a convex k-gon. Later in 1961, they constructed a point set of size 2k−2 not containing the vertex set of any convex k-gon. This leads to what is known as the Erdős-Szekeres Conjecture, that any point set of 2k−2 + 1 points contains the vertices of a convex k-gon. Recently, this fa...
متن کاملDensity of the Periodic Points in the Interval Set
The dynamical system (f,R) is introduced and some of its properties are investigated. It is proven that there is an invariant set Λ on which the periodic points of f are dense.
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1987
ISSN: 0196-8858
DOI: 10.1016/0196-8858(87)90020-0