G. Petridis

activity

20112026

most citedNew results on sum-product type growth over fields

52 citations · 208 across the 22 of their papers we have counts for

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22 papers · 1 filter

math.CO2026

Refined upper bounds on Schur-like numbers

Swaroop Hegde, Andrew Lott, Giorgis Petridis +1

For positive integers $r, m$ and $N$ , every $r$ -coloring of ${1, \dots, N}$ contains a monochromatic solution to $x_{1} + \dots + x_{m + 1} = y_{1} + \dots + y_{m}$ provided that $N \ge 3^r (r!)^{…

math.CO2021★ 2 cited

Almost orthogonal subsets of vector spaces over finite fields

Ali Mohammadi, Giorgis Petridis

We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In parti…

math.CO2020

A question of Bukh on sums of dilates

Brandon Hanson, Giorgis Petridis

We answer in the affirmative a question of Bukh on the cardinality of the dilate sum $A + 2 \cdot A$ .

math.CO2020★ 3 cited

Bounds of Trilinear and Trinomial Exponential Sums

Simon Macourt, Giorgis Petridis, Ilya D. Shkredov +1

We prove, for a sufficiently small subset $A$ of a prime residue field, an estimate on the number of solutions to the equation $(a_{1} - a_{2}) (a_{3} - a_{4}) = (a_{5} - a_{6}) (a_{7} - a_{8})$ w…

math.CO2020★ 29 cited

On the Pinned Distances Problem in Positive Characteristic

Brendan Murphy, Giorgis Petridis, Thang Pham +2

We study the Erd\H os-Falconer distance problem for a set $A \subset F^{2}$ , where $F$ is a field of positive characteristic $p$ . If $F = F_{p}$ and th…

math.CO2019★ 2 cited

An Energy Bound in the Affine Group

Giorgis Petridis, Oliver Roche-Newton, Misha Rudnev +1

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 a…

math.CO2019★ 9 cited

An example related to the Erdos-Falconer question over arbitrary finite fields

Brendan Murphy, Giorgis Petridis

There exists an infinite family of examples of subsets of $F_{q}^{2}$ with $q^{4/3}$ elements whose distance sets are not the whole of $F_{q}$ .

math.CO2018★ 7 cited

Bisectors and pinned distances

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…

math.CO2017★ 3 cited

Products of Differences over Arbitrary Finite Fields

Brendan Murphy, Giorgis Petridis

There exists an absolute constant $δ > 0$ such that for all $q$ and all subsets $A \subseteq F_{q}$ of the finite field with $q$ elements, if $∣ A ∣ > q^{2/3 - δ}$ , then \[ |(A…

math.CO2017★ 52 cited

New results on sum-product type growth over fields

Brendan Murphy, Giorgis Petridis, Oliver Roche-Newton +2

We prove a range of new sum-product type growth estimates over a general field $F$ , in particular the special case $F = F_{p}$ . They are unified by the theme…

math.CO2017★ 3 cited

A Second Wave of Expanders over Finite Fields

Brendan Murphy, Giorgis Petridis

This is an expository survey on recent sum-product results in finite fields. We present a number of sum-product or "expander" results that say that if $∣ A ∣ > p^{2/3}$ then some set…

math.CO2016★ 4 cited

Collinear triples and quadruples for Cartesian products in $F_{p}^{2}$

Giorgis Petridis

In this ote, which has been absorbed by arXiv1702.01003, we combine a recent point-line incidence bound of Stevens and de Zeeuw with an older lemma of Bourgain, Katz and Tao to bou…

math.CO2016

Pinned algebraic distances determined by Cartesian products in $F_{p}^{2}$

Giorgis Petridis

Let $p$ be an odd prime and $A \subseteq F_{p}$ be a subset of the finite field with $p$ elements. We show that $A \times A \subseteq F_{p}^{2}$ determines at least a c…

math.CO2016★ 9 cited

A point-line incidence identity in finite fields, and applications

Brendan Murphy, Giorgis Petridis

Let $E \subseteq F_{q}^{2}$ be a set in the 2-dimensional vector space over a finite field with $q$ elements. We prove an identity for the second moment of its incidence funct…

math.CO2016★ 14 cited

Products of Differences in Prime Order Finite Fields

Giorgis Petridis

There exists an absolute constant $C$ with the following property. Let $A \subseteq F_{p}$ be a set in the prime order finite field with $p$ elements. Suppose that $|A| > C…

math.CO2015

On the Number of Dot Products Determined by a Large Set and One of its Translates in Finite Fields

Giorgis Petridis

Let $E \subseteq F_{q}^{2}$ be a set in the 2-dimensional vector space over a finite field with $q$ elements, which satisfies $∣ E ∣ > q$ . There exist $x, y \in E$ such that $|E…

math.CO2013

The Cardinality of Sumsets: Different Summands

Brendan Murphy, Eyvindur Ari Palsson, Giorgis Petridis

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…

math.CO2012

Matchings in Random Biregular Bipartite Graphs

Guillem Perarnau, Giorgis Petridis

We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdos and…

math.CO2011

The L^1-norm of exponential sums in Z^d

Giorgis Petridis

Let A be a finite set of integers and F_A its exponential sum. McGehee, Pigno & Smith and Konyagin have independently proved that the L^1-norm of F_A is at least c log|A| for some…

math.CO2011

Upper Bounds on the Cardinality of Higher Sumsets

Giorgis Petridis

Let A and B be finite sets in a commutative group. We bound |A+hB| in terms of |A|, |A+B| and h. We provide a submultiplicative upper bound that improves on the existing bound of I…

math.CO2011★ 36 cited

New Proofs of Plünnecke-type Estimates for Product Sets in Groups

Giorgis Petridis

We present a new method to bound the cardinality of triple product sets in groups and give three applications. A new and unexpectedly short proof of the Plunnecke-Ruzsa sumset ineq…

math.CO2011

Plünnecke's Inequality

Giorgis Petridis

Plunnecke's inequality is the standard tool to obtain estimates on the cardinality of sumsets and has many applications in additive combinatorics. We present a new proof. The main…

Refined upper bounds on Schur-like numbers

Almost orthogonal subsets of vector spaces over finite fields

A question of Bukh on sums of dilates

Bounds of Trilinear and Trinomial Exponential Sums

On the Pinned Distances Problem in Positive Characteristic

An Energy Bound in the Affine Group

An example related to the Erdos-Falconer question over arbitrary finite fields

Bisectors and pinned distances

Products of Differences over Arbitrary Finite Fields

New results on sum-product type growth over fields

A Second Wave of Expanders over Finite Fields

Collinear triples and quadruples for Cartesian products in Fp2​

Pinned algebraic distances determined by Cartesian products in Fp2​

A point-line incidence identity in finite fields, and applications

Products of Differences in Prime Order Finite Fields

On the Number of Dot Products Determined by a Large Set and One of its Translates in Finite Fields

The Cardinality of Sumsets: Different Summands

Matchings in Random Biregular Bipartite Graphs

The L^1-norm of exponential sums in Z^d

Upper Bounds on the Cardinality of Higher Sumsets

New Proofs of Plünnecke-type Estimates for Product Sets in Groups

Plünnecke's Inequality

Collinear triples and quadruples for Cartesian products in $F_{p}^{2}$

Pinned algebraic distances determined by Cartesian products in $F_{p}^{2}$