Zobrazeno 1 - 10
of 17
pro vyhledávání: '"David Covert"'
Autor:
David Covert
Publikováno v:
Carus Mathematical Monographs ISBN: 9781470467739
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::880b7fbedf138011a9315b206be84a67
https://doi.org/10.1090/car/037
https://doi.org/10.1090/car/037
Publikováno v:
Graphs and Combinatorics. 35:393-417
We explore a paradigm which ties together seemingly disparate areas in number theory, additive combinatorics, and geometric combinatorics including the classical Waring problem, the Furstenberg–Sarkozy theorem on squares in sets of integers with po
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::191b29f01998b53978053add669b3aec
https://doi.org/10.1007/s00373-018-2002-9
https://doi.org/10.1007/s00373-018-2002-9
Autor:
Derrick Hart, Michael Bennett, Jeremy Chapman, Jonathan Pakianathan, David Covert, Alex Iosevich
Publikováno v:
Journal of the Korean Mathematical Society. 53:115-126
Let $E \subset {\Bbb F}_q^d$, the $d$-dimensional vector space over a finite field with $q$ elements. Construct a graph, called the distance graph of $E$, by letting the vertices be the elements of $E$ and connect a pair of vertices corresponding to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cb13ec1eed725a4b3b8548e7f23113dd
https://doi.org/10.4134/jkms.2016.53.1.115
https://doi.org/10.4134/jkms.2016.53.1.115
Autor:
David Covert
Publikováno v:
Journal of Mathematical Analysis and Applications. 426:727-733
The Erdős–Falconer distance problem in Z q d asks one to show that if E ⊂ Z q d is of sufficiently large cardinality, then the set of distances determined by E satisfies Δ ( E ) = Z q . Previous results were known only in the case q = p l , whe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0d17d27ca394ed0bb9a9c5a9bbb29256
https://doi.org/10.1016/j.jmaa.2015.01.063
https://doi.org/10.1016/j.jmaa.2015.01.063
Let $${\mathbb {F}}_q^d$$ be the d-dimensional vector space over the finite field $${\mathbb {F}}_q$$ with q elements. Given k sets $$E_j\subset {\mathbb {F}}_q^d$$ for $$j=1,2,\ldots , k$$ , the generalized k-resultant modulus set, denoted by $$\Del
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7df35e09c1daf9df9be5753efe9dfa70
Publikováno v:
Discrete Mathematics. 311:423-430
We show that if E@?F"q^d, the d-dimensional vector space over the finite field with q elements, and |E|>=@rq^d, where q^-^1^2@?@r@?1, then E contains an isometric copy of at least c@r^d^-^1q^d^+^1^2 distinct (d+1)-point configurations.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2aad3381860f9a413f6aa1e979681a8f
https://doi.org/10.1016/j.disc.2010.10.009
https://doi.org/10.1016/j.disc.2010.10.009
Publikováno v:
European Journal of Combinatorics. 31:306-319
In recent years, sum-product estimates in Euclidean space and finite fields have received great attention. They can often be interpreted in terms of Erdos type incidence problems involving the distribution of distances, dot products, areas, and so on
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ae1fb6d1588185afcb27a8fdf56548fd
https://doi.org/10.1016/j.ejc.2008.11.015
https://doi.org/10.1016/j.ejc.2008.11.015
We study the k-resultant modulus set problem in the d-dimensional vector space F q d over the finite field F q with q elements. Given E ⊂ F q d and an integer k ≥ 2 , the k-resultant modulus set, denoted by Δ k ( E ) , is defined as Δ k ( E ) =
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a74be32d6eebee716f583a5931f96630
http://arxiv.org/abs/1508.02688
http://arxiv.org/abs/1508.02688
For a set $E\subset \mathbb F_q^d$, we define the $k$-resultant magnitude set as $ \Delta_k(E) =\{\|\textbf{x}_1 + \dots + \textbf{x}_k\|\in \mathbb F_q: \textbf{x}_1, \dots, \textbf{x}_k \in E\},$ where $\|\textbf{v}\|=v_1^2+\cdots+ v_d^2$ for $\tex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2f54f300dbaae433fa83d32dc08af85a
http://arxiv.org/abs/1403.6138
http://arxiv.org/abs/1403.6138