Zobrazeno 1 - 10
of 46
pro vyhledávání: '"Milićević, Luka"'
Autor:
Milićević, Luka
The inverse theory for Gowers uniformity norms is one of the central topics in additive combinatorics and one of the most important aspects of the theory is the question of bounds. In this paper, we prove a quasipolynomial inverse theorem for the $\m
Externí odkaz:
http://arxiv.org/abs/2410.08966
Autor:
Milićević, Luka
A skew corner is a triple of points in $\mathbb{Z} \times \mathbb{Z}$ of the form $(x,y), (x, y + a)$ and $(x + a, y')$. Pratt posed the following question: how large can a set $A \subseteq [n] \times [n]$ be, provided it contains no non-trivial skew
Externí odkaz:
http://arxiv.org/abs/2404.07180
Autor:
Baber, Rahil, Behague, Natalie, Calbet, Asier, Ellis, David, Erde, Joshua, Gray, Ron, Ivan, Maria-Romina, Janzer, Barnabás, Johnson, Robert, Milićević, Luka, Talbot, John, Tan, Ta Sheng, Wickes, Belinda
One of the great pleasures of working with Imre Leader is to experience his infectious delight on encountering a compelling combinatorial problem. This collection of open problems in combinatorics has been put together by a subset of his former PhD s
Externí odkaz:
http://arxiv.org/abs/2310.18163
Autor:
Milićević, Luka
Let $G$ and $H$ be finite-dimensional vector spaces over $\mathbb{F}_p$. A subset $A \subseteq G \times H$ is said to be transverse if all of its rows $\{x \in G \colon (x,y) \in A\}$, $y \in H$, are subspaces of $G$ and all of its columns $\{y \in H
Externí odkaz:
http://arxiv.org/abs/2308.15175
Autor:
Milićević, Luka
A classical result in additive combinatorics, which is a combination of Balog-Szemer\'edi-Gowers theorem and a variant of Freiman's theorem due to Ruzsa, says that if a subset $A$ of $\mathbb{F}_p^n$ contains at least $c |A|^3$ additive quadruples, t
Externí odkaz:
http://arxiv.org/abs/2308.12881
Autor:
Milićević, Luka
We prove quantitative bounds for the inverse theorem for Gowers uniformity norms $\mathsf{U}^5$ and $\mathsf{U}^6$ in $\mathbb{F}_2^n$. The proof starts from an earlier partial result of Gowers and the author which reduces the inverse problem to a st
Externí odkaz:
http://arxiv.org/abs/2207.01591
Autor:
Milićević, Luka
Let $V$ be a finite-dimensional vector space over $\mathbb{F}_p$. We say that a multilinear form $\alpha \colon V^k \to \mathbb{F}_p$ in $k$ variables is $d$-approximately symmetric if the partition rank of difference $\alpha(x_1, \dots, x_k) - \alph
Externí odkaz:
http://arxiv.org/abs/2112.14755
Autor:
Milićević, Luka
Let $G$ be a finite-dimensional vector space over a prime field $\mathbb{F}_p$ with some subspaces $H_1, \dots, H_k$. Let $f \colon G \to \mathbb{C}$ be a function. Generalizing the notion of Gowers uniformity norms, Austin introduced directional Gow
Externí odkaz:
http://arxiv.org/abs/2103.06354
Autor:
Milićević, Luka
Let $G_1, \dots, G_k$ be vector spaces over a finite field $\mathbb{F} = \mathbb{F}_q$ with a non-trivial additive character $\chi$. The analytic rank of a multilinear form $\alpha \colon G_1 \times \dots \times G_k \to \mathbb{F}$ is defined as $\op
Externí odkaz:
http://arxiv.org/abs/1902.09830
Autor:
Milićević, Luka
For a positive integer $r$, let $G(r)$ be the smallest $N$ such that, whenever the edges of the Cartesian product $K_N \times K_N$ are $r$-coloured, then there is a rectangle in which both pairs of opposite edges receive the same colour. In this pape
Externí odkaz:
http://arxiv.org/abs/1809.09458