# Letícia Mattos's research while affiliated with Freie Universität Berlin and other places

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## Publications (10)

Let $X_H$ be the number of copies of a fixed graph $H$ in $G(n,p)$. In 2016, Gilmer and Kopparty conjectured that a local central limit theorem should hold for $X_H$ as long as $H$ is connected, $p \gg n^{-1/m(H)}$ and $n^2(1-p)\gg 1$. Recently, Sah and Sahwney showed that the Gilmer--Kopparty conjecture holds for constant $p$. In this paper, we sh...

One of the major problems in combinatorics is to determine the number of r-uniform hypergraphs (r-graphs) on n vertices which are free of certain forbidden structures. This problem dates back to the work of Erdős, Kleitman and Rothschild, who showed that the number of Kr-free graphs on n vertices is 2ex(n,Kr)+o(n2). Their work was later extended to...

An essential cover of the vertices of the $n$-cube $\{0,1\}^n$ by hyperplanes is a minimal covering where no hyperplane is redundant and every variable appears in the equation of at least one hyperplane. Linial and Radhakrishnan gave a construction of an essential cover with $\lceil \frac{n}{2} \rceil + 1$ hyperplanes and showed that $\Omega(\sqrt{...

We say that G→(F,H)$$ G\to \left(F,H\right) $$ if, in every edge coloring c:E(G)→{1,2}$$ c:E(G)\to \left\{1,2\right\} $$, we can find either a 1‐colored copy of F$$ F $$ or a 2‐colored copy of H$$ H $$. The well‐known states that the threshold for the property G(n,p)→(F,H)$$ G\left(n,p\right)\to \left(F,H\right) $$ is equal to n−1/m2(F,H)$$ {n}^{-1...

For graphs $G$ and $H$, we write $G \overset{\mathrm{rb}}{\longrightarrow} H $ if any proper edge-coloring of $G$ contains a rainbow copy of $H$, i.e., a copy where no color appears more than once. Kohayakawa, Konstadinidis and the last author proved that the threshold for $G(n,p) \overset{\mathrm{rb}}{\longrightarrow}H$ is at most $n^{-1/m_2(H)}$....

One of the major problems in combinatorics is to determine the number of $r$-uniform hypergraphs ($r$-graphs) on $n$ vertices which are free of certain forbidden structures. This problem dates back to the work of Erd\H{o}s, Kleitman and Rothschild, who showed that the number of $K_r$-free graphs on $n$ vertices is $2^{\text{ex}(n,K_r)+o(n^2)}$. The...

We say that $G \to (F,H)$ if, in every edge colouring $c: E(G) \to \{1,2\}$, we can find either a $1$-coloured copy of $F$ or a $2$-coloured copy of $H$. The well-known Kohayakawa--Kreuter conjecture states that the threshold for the property $G(n,p) \to (F,H)$ is equal to $n^{-1/m_{2}(F,H)}$, where $m_{2}(F,H)$ is given by \[ m_{2}(F,H):= \max \le...

A well-known conjecture states that a random symmetric $n \times n$ matrix with entries in $\{-1,1\}$ is singular with probability $\Theta\big( n^2 2^{-n} \big)$. In this paper we prove that the probability of this event is at most $\exp\big( - \Omega( \sqrt{n} ) \big)$, improving the best known bound of $\exp\big( - \Omega( n^{1/4} \sqrt{\log n} )...

## Citations

... Section 2 was first written in May 2015, predating a recent paper of Geneson [41] showing that T k ≤ k 5/2+o (1) . More recently J. Balogh, W. Linz and L. Mattos [9] independently investigated the question of estimating T k and showed that T k = k 2+o(1) (which is slightly weaker than Corollary 2.4). We would like to thank Kevin Ford for some helpful discussions on this theme and also thank the anonymous referees for their careful reading of the paper and useful suggestions. ...

Reference: Short proofs of some extremal results III

... Such an optimal estimate is not yet known for the symmetric Bernoulli matrix B n (even though it is conjectured) but the paper [32] proves that the probability that it is singular is bounded above by e O. ...

Reference: Bernoulli random matrices

... This is achieved in the paper of Marciniszyn, Skokan, Spöhel and Steger [23] which deals with the case when H 1 and H 2 are both cliques (and not both K 3 ), albeit with different methods. In [18] and [22], which deal with the cases when H 1 and H 2 are both cycles and H 1 and H 2 are a clique and a cycle, respectively, the authors of both papers show implicitly thatB(H 1 , H 2 ) = ∅. Let us also remark that in [23], it is implicitly shown thatB(H 1 , H 2 ) with each H i a clique, is non-empty only when H 2 = K 3 or H 1 = H 2 = K 4 , and moreover, |B(H 1 , H 2 )| ≤ 3 in each case. ...