Zobrazeno 1 - 10
of 119
pro vyhledávání: '"Sauermann, Lisa"'
We prove new lower bounds on the maximum size of subsets $A\subseteq \{1,\dots,N\}$ or $A\subseteq \mathbb{F}_p^n$ not containing three-term arithmetic progressions. In the setting of $\{1,\dots,N\}$, this is the first improvement upon a classical co
Externí odkaz:
http://arxiv.org/abs/2406.12290
We prove new lower bounds on the maximum size of sets $A\subseteq \mathbb{F}_p^n$ or $A\subseteq \mathbb{Z}_m^n$ not containing three-term arithmetic progressions (consisting of three distinct points). More specifically, we prove that for any fixed i
Externí odkaz:
http://arxiv.org/abs/2401.12802
Autor:
Kwan, Matthew, Sauermann, Lisa
Consider a quadratic polynomial $Q(\xi_{1},\dots,\xi_{n})$ of independent Rademacher random variables $\xi_{1},\dots,\xi_{n}$. To what extent can $Q(\xi_{1},\dots,\xi_{n})$ concentrate on a single value? This quadratic version of the classical Little
Externí odkaz:
http://arxiv.org/abs/2312.13826
Autor:
Sauermann, Lisa, Xu, Zixuan
We prove a new lower bound for the almost 20 year old problem of determining the smallest possible size of an essential cover of the $n$-dimensional hypercube $\{\pm 1\}^n$, i.e. the smallest possible size of a collection of hyperplanes that forms a
Externí odkaz:
http://arxiv.org/abs/2310.05775
Autor:
Sauermann, Lisa, Zakharov, Dmitrii
We prove essentially sharp bounds for Ramsey numbers of ordered hypergraph matchings, inroduced recently by Dudek, Grytczuk, and Ruci\'{n}ski. Namely, for any $r \ge 2$ and $n \ge 2$, we show that any collection $\mathcal H$ of $n$ pairwise disjoint
Externí odkaz:
http://arxiv.org/abs/2309.04813
An edge-coloured graph is said to be rainbow if no colour appears more than once. Extremal problems involving rainbow objects have been a focus of much research over the last decade as they capture the essence of a number of interesting problems in a
Externí odkaz:
http://arxiv.org/abs/2309.04460
Autor:
Sauermann, Lisa, Zakharov, Dmitrii
The Erd\H{o}s--Ginzburg--Ziv Problem is a classical extremal problem in discrete geometry. Given $m$ and $n$, the problem asks about the smallest number $s$ such that among any $s$ points in the integer lattice $\mathbb{Z}^n$ one can find $m$ points
Externí odkaz:
http://arxiv.org/abs/2302.14737
Erd\H{o}s' unit distance problem and Erd\H{o}s' distinct distances problem are among the most classical and well-known open problems in discrete mathematics. They ask for the maximum number of unit distances, or the minimum number of distinct distanc
Externí odkaz:
http://arxiv.org/abs/2302.09058
Autor:
Li, Anqi, Sauermann, Lisa
In this paper, we strengthen a result by Green about an analogue of Sarkozy's theorem in the setting of polynomial rings $\mathbb{F}_q[x]$. In the integer setting, for a given polynomial $F \in \mathbb{Z}[x]$ with constant term zero, (a generalizatio
Externí odkaz:
http://arxiv.org/abs/2212.12754
Suppose we are given matchings $M_1,....,M_N$ of size $t$ in some $r$-uniform hypergraph, and let us think of each matching having a different color. How large does $N$ need to be (in terms of $t$ and $r$) such that we can always find a rainbow match
Externí odkaz:
http://arxiv.org/abs/2212.07580