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Showing 1 to 12 of 12 for “"Arithmetic Progression"”.
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Topics in Analytic, Combinatorial and Probabilistic Number Theory
… of {l, ..., N} of size M contains at least one arithmetic progression of length k. We also investigate the length of the longest arithmetic progression in a random subset of positive integers.
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Fourier decoupling for convex sequences
… with frequency support in a neigh- borhood of an arithmetic progression.
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An Exposition Of Dirichlet’s Theorem
… the location and size of the prime numbers. Arithmetic progressions are very easily described subsets of the integers, yet they are infinite so it might be the case that they contain infinitely many prime numbers. Using Euclid’s original proof of the infiniteness of the primes as a model, we …
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Extremal graph theory: supersaturation and enumeration
… of subsets of [n] which does not contain an arithmetic progression of a fixed length. This addresses another question of Cameron and Erdos and provides an optimal bound for infinitely many n. As corollaries, we improve the known transference results on arithmetic progressions.
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Product Structure, Separating Systems, Freeze-Tag Problem, and Planar Multicolor Turan Number
… using Behrend’s construction for three-term arithmetic progression-free sets. Together, these works contribute to both theoretical and algorithmic advancements in graph decompositions, separating systems, and optimization problems within geometric and graph theoretic settings.
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Distribution of Farey Series and Free Path Lengths for a Certain Billiard in the Unit Square
… of FQ with denominators belonging to a fixed arithmetic progression. Following Niederreiter, Dress, and Huxley, we establish a best possible estimate for the absolute discrepancy of these subsets in short intervals. Second, in relating the foregoing result to the distribution of visible points …
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Detection of statistical differences between visual textures as a function of mean dot density
… conditions were used; three were based on an arithmetic progression and one on a logarithmic progression, i.e. mean densities 9, 12, 15 and 12 (log). It was felt that the use of a logarithmic progression in the construction of the patterns would facilitate the detection task. The displays …
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Topics in number theory
… г(s/2) ζ (s). The remaining topics are more arithmetic in nature. An attempt is made to show by elementary methods that the order of the Tchebychef difference ψ(x) - x is not greater than that of the Möbius sum M(x), and although only partially successful, the attempt improves on previously …
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The Factoradic Integers
The arithmetic progressions under addition and composition satisfy the usual rules of arithmetic with a modified distributive law. The basic algebra of such mathematical structures is examined; this leads to the consideration of the integers as a metric space under the "factoradic metric", i.e., …
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Games, Graphs, and Groups
… that every configuration containing a 4-term arithmetic progression is uncommon in $\mathbb{F}_p^n$ for primes $p\geq 5$ and large $n$ and in $\mathbb{Z}_p$ for large primes $p$. We call a graph $H$ *strongly common* if for every colouring $\phi$ of $K_n$ with two colours, the number of …
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On Refinements of Van der Waerden's Theorem
We examine different methods of generalize Van der Waerden's Theorem, the Multidimensional Van der Waerden Theorem, the Canonical Van der Waerden Theorem, and other Variants.