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In additive number theory, a way to measure how dense a sequence of numbers is
In additive number theory, the Schnirelmann density of a sequence of numbers is a way to measure how "dense" the sequence is. It is named after Soviet
Schnirelmann_density
Concept in number theory
natural density makes this intuition precise for many, but not all, subsets of the naturals (see Schnirelmann density, which is similar to natural density but
Natural_density
Soviet mathematician (1905–1938)
107-108 Inscribed square problem Schnirelmann density Schnirelmann's constant Schnirelmann's theorem Schnirelmann, L.G. (1930). "On the additive properties
Lev_Schnirelmann
Mann according to which the Schnirelmann density of a sum of two sequences is at least the sum of their Schnirelmann densities, unless their sum consists
Additive_basis
Operation on pairs of integer sequences
developed by Freeman Dyson as part of his proof of Mann's theorem on the Schnirelmann density of sumsets, is used to prove such fundamental results of additive
Dyson's_transform
Even integers as sums of two primes
computable constant; see Schnirelmann density. Schnirelmann's constant is the lowest number C with this property. Schnirelmann himself obtained C < 800000
Goldbach's_conjecture
Topics referred to by the same term
Optical density, the absorbance of a material Natural density, also called asymptotic density Dirichlet density Schnirelmann density Density (polytope)
Density_(disambiguation)
Sequence of numbers avoiding sums of subsets
from the fact that sum-free sequences are small that they have zero Schnirelmann density; that is, if A ( x ) {\displaystyle A(x)} is defined to be the number
Sum-free_sequence
Mathematical problem in number theory
ISBN 978-0-486-40026-6. Has an elementary proof of the existence of G(k) using Schnirelmann density. Nathanson, Melvyn B. (1996). Additive Number Theory: The Classical
Waring's_problem
theorem Taxicab number Generalized taxicab number Cabtaxi number Schnirelmann density Sumset Landau–Ramanujan constant Sierpinski number Seventeen or Bust
List_of_number_theory_topics
Sums vector sets A and B by adding each vector in A to each vector in B
sumset – Sumset of a field subject to a specific polynomial restriction Schnirelmann density – In additive number theory, a way to measure how dense a sequence
Minkowski_addition
One of several related theorems regarding the sizes of certain sumsets in abelian groups
Mann's theorem on Schnirelmann density. If C {\displaystyle C} is a subset of N {\displaystyle \mathbb {N} } , the lower asymptotic density of C {\displaystyle
Kneser's theorem (combinatorics)
Kneser's_theorem_(combinatorics)
Mathematical monograph
including Mann's theorem that the Schnirelmann density of a sumset is at least the sum of the Schnirelmann densities and Kneser's theorem on the structure
Sequences_(book)
Mathematical subject
Ergodic Ramsey theory Problems involving arithmetic progressions Schnirelmann density Shapley–Folkman lemma Sidon set Sum-free set Restricted sumset Sum-product
Arithmetic_combinatorics
differential equations Lev Schnirelmann, developed the Lusternik–Schnirelmann category in topology and Schnirelmann density of numbers Igor Shafarevich
List of Russian mathematicians
List_of_Russian_mathematicians
Soviet mathematician (1915–1972)
influential). An elementary proof of the Hilbert-Waring theorem; see also Schnirelmann density. The Linnik ergodic method, see Linnik (1968), which allowed him
Yuri_Linnik
contributions to computer sciences Lev Schnirelmann, developed the Lusternik–Schnirelmann category in topology and Schnirelmann density of numbers Moses Schönfinkel
List_of_Russian_scientists
zero Natural density Negligible set Nowhere dense set Null set, conull set Partition regular Piecewise syndetic set Schnirelmann density Small set (combinatorics)
List of exceptional set concepts
List_of_exceptional_set_concepts
principle in optimal control Lev Schnirelmann, developed the Lusternik–Schnirelmann category in topology and Schnirelmann density of numbers Moses Schönfinkel
List_of_Russian_people
Form of differential geometry
journals. For example, a connection of systolic category with the Lusternik–Schnirelmann category has emerged. The existence of such a link can be thought of
Systolic_geometry
Mathematician and statistician (1905–2000)
students. In additive number theory, Mann proved the Schnirelmann–Landau conjecture on the asymptotic density of sumsets in 1942. By doing so he established
Henry_Mann
Geopolitical region in Azerbaijan
there were still Armenian villages in the region". Historian Victor Schnirelmann writes that "In the mid-18th century, … Turkic tribes … gained access
Nagorno-Karabakh
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