Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Giorgis Petridis"'
Autor:
Brandon Hanson, Giorgis Petridis
Publikováno v:
Discrete Analysis (2021)
A question of Bukh on sums of dilates, Discrete Analysis 2021:13, 21 pp. Let $A$ and $B$ be subsets of an Abelian group. Their sumset $A+B$ is defined to be the set of all $a+b$ such that $a\in A$ and $b\in B$. Many questions in additive combinatori
Externí odkaz:
https://doaj.org/article/0e27120813d34557b7af7cc1aa578c19
Autor:
Brendan Murphy, Giorgis Petridis
Publikováno v:
Discrete Analysis (2018)
Products of Differences over Arbitrary Finite Fields, Discrete Analysis 2018:18, 42 pp. A central problem in arithmetic combinatorics is the Erdős-Szemerédi sum-product problem, which asks whether it is true that if $A$ is a finite set of integers
Externí odkaz:
https://doaj.org/article/a88eb8b4abb54a9da1cefa2c9532002a
Publikováno v:
International Mathematics Research Notices. 2022:1154-1172
We prove a nontrivial energy bound for a finite set of affine transformations over a general field and discuss a number of implications. These include new bounds on growth in the affine group, a quantitative version of a theorem by Elekes about rich
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::677e32ef297aa8e73ce26667ad9264f8
https://doi.org/10.1093/imrn/rnaa130
https://doi.org/10.1093/imrn/rnaa130
Publikováno v:
SIAM Journal on Discrete Mathematics. 34:2124-2136
We prove, for a sufficiently small subset $\mathcal{A}$ of a prime residue field, an estimate on the number of solutions to the equation $(a_1-a_2)(a_3-a_4) = (a_5-a_6)(a_7-a_8)$ with all variables in $\mathcal{A}$. We then derive new bounds on trili
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e9c9eb826979a23f23e0c96515b0e472
https://doi.org/10.1137/20m1325502
https://doi.org/10.1137/20m1325502
Autor:
Giorgis Petridis, Igor E. Shparlinski
Publikováno v:
Journal d'Analyse Mathématique. 138:613-641
We use an estimate of Aksoy Yazici, Murphy, Rudnev and Shkredov (2016) on the number of solutions of certain equations involving products and differences of sets in prime finite fields to give an explicit upper bound on trilinear exponential sums whi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9ede0479eb5fd49ee66630180275daa9
https://doi.org/10.1007/s11854-019-0028-4
https://doi.org/10.1007/s11854-019-0028-4
We study the Erd\H os-Falconer distance problem for a set $A\subset \mathbb{F}^2$, where $\mathbb{F}$ is a field of positive characteristic $p$. If $\mathbb{F}=\mathbb{F}_p$ and the cardinality $|A|$ exceeds $p^{5/4}$, we prove that $A$ determines an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0e1b884e6522ef592c3ffba8ba7c9e2f
http://arxiv.org/abs/2003.00510
http://arxiv.org/abs/2003.00510
Autor:
Giorgis Petridis
Publikováno v:
Combinatorics and Finite Fields
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::677951879adf92e58290437d9e7d1bb9
https://doi.org/10.1515/9783110642094-010
https://doi.org/10.1515/9783110642094-010
Autor:
Giorgis Petridis, Brandon Hanson
We prove that the clique number of the Paley graph is at most $\sqrt{p/2} + 1$, and that any supposed additive decompositions of the set of quadratic residues can only come from co-Sidon sets.
7 pages. The second version already included a corol
7 pages. The second version already included a corol
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5e11f1dca2fe98ecc4520215c8efaaf0
http://arxiv.org/abs/1905.09134
http://arxiv.org/abs/1905.09134
Autor:
Ben Lund, Giorgis Petridis
We prove, under suitable conditions, a lower bound on the number of pinned distances determined by small subsets of two-dimensional vector spaces over fields. For finite subsets of the Euclidean plane we prove an upper bound for their bisector energy
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::333c9bf319132e925d03a31be4b7a1e8
http://arxiv.org/abs/1810.00765
http://arxiv.org/abs/1810.00765
Publikováno v:
Acta Arithmetica. 167:375-395
Let $h$ be a positive integer and $A, B_1, B_2,\dots, B_h$ be finite sets in a commutative group. We bound $|A+B_1+...+B_h|$ from above in terms of $|A|, |A+B_1|,\dots,|A+B_h|$ and $h$. Extremal examples, which demonstrate that the bound is asymptoti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ebcbd0fc83aa7d93e9dfae530ef1c984
https://doi.org/10.4064/aa167-4-4
https://doi.org/10.4064/aa167-4-4