Sets with large additive energy and symmetric sets
نویسندگان
چکیده
منابع مشابه
Sets with large additive energy and symmetric sets
We show that for any set A in a finite Abelian group G that has at least c|A|3 solutions to a1 + a2 = a3 + a4, ai ∈ A there exist sets A ′ ⊆ A and Λ ⊆ G, Λ = {λ1, . . . , λt}, t ≪ c −1 log |A| such that A′ is contained in {∑t j=1 εjλj | εj ∈ {0,−1, 1} } and A′ has ≫ c|A|3 solutions to a1 + a ′ 2 = a ′ 3 + a ′ 4, a ′ i ∈ A ′. We also study so–called symmetric sets or, in other words, sets of lar...
متن کاملFinite Sets and Symmetric Simplicial Sets
The category of finite cardinals (or, equivalently, of finite sets) is the symmetric analogue of the category of finite ordinals, and the ground category of a relevant category of presheaves, the augmented symmetric simplicial sets. We prove here that this ground category has characterisations similar to the classical ones for the category of finite ordinals, by the existence of a universal sym...
متن کاملFinding large co-Sidon subsets in sets with a given additive energy
For two finite sets of integers A and B their additive energy E(A, B) is the number of solutions to a + b = a + b, where a, a ∈ A and b, b ∈ B. Given finite sets A, B ⊆ Z with additive energy E(A, B) = |A||B| + E, we investigate the sizes of largest subsets A ⊆ A and B ⊆ B with all |A||B| sums a + b, a ∈ A, b ∈ B, being different (we call such subsets A, B co-Sidon). In particular, for |A| = |B...
متن کاملThe symmetric monoidal closed category of cpo $M$-sets
In this paper, we show that the category of directed complete posets with bottom elements (cpos) endowed with an action of a monoid $M$ on them forms a monoidal category. It is also proved that this category is symmetric closed.
متن کاملLarge Sets of Noncospectral Graphs with Equal Laplacian Energy
Several alternative definitions to graph energy have appeared in literature recently, the first among them being the Laplacian energy, defined by Gutman and Zhou in [Linear Algebra Appl. 414 (2006), 29–37]. We show here that Laplacian energy apparently has small power of discrimination among threshold graphs, by showing that, for each n, there exists a set of n mutually noncospectral connected ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2011
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2010.11.001