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Ramsey Graphs Induce Subgraphs of Many Different Sizes
TLDR
A graph on n vertices is said to be C-Ramsey if every clique or independent set of the graph induces subgraphs of at least n2-o(1) distinct sizes. Expand
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Counting Zeros of Cosine Polynomials: On a Problem of Littlewood
We show that if $A$ is a finite set of non-negative integers then the number of zeros of the function \[ f_A(\theta) = \sum_{a \in A} \cos(a\theta), \] in $[0,2\pi]$, is at least $(\log \log \logExpand
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Dense subgraphs in random graphs
TLDR
We show that $\omega_{\gamma}(G_{n,p})$ is concentrated on a set of two integers. Expand
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A stability theorem for maximal Kr+1-free graphs
TLDR
For $r \geq 2$, we show that every maximal $K_{r+1}$-free graph $G$ on $n$ vertices with $(1-\frac{1}{r})\frac{n^2}{2}-o(n^{\frac{r+ 1}{r}})$ edges contains a complete $r$-partite subgraph on $(1 - o(1))n$. Expand
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Partitioning a graph into monochromatic connected subgraphs
TLDR
A well-known result by Haxell and Kohayakawa states that the vertices of an $r$-coloured complete graph can be partitioned into $r-1$ monochromatic connected subgraphs of distinct colours; this is a slightly weaker variant of a conjecture by Erdős, Pyber and Gyarfas. Expand
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On Abelian and Additive Complexity in Infinite Words
TLDR
In this note we define bounded additive complexity for infinite words over a finite subset of . Expand
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On the Maximum Running Time in Graph Bootstrap Percolation
TLDR
Graph bootstrap percolation is a simple cellular automaton introduced by Bollob\'as in 1968. Expand
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On a New Idiom in the Study of Entailment
This paper is an experiment in Leibnizian analysis. The reader will recall that Leibniz considered all true sentences to be analytically so. The difference, on his account, between necessary andExpand
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Central limit theorems from the roots of probability generating functions
For each $n$, let $X_n \in \{0,\ldots,n\}$ be a random variable with mean $\mu_n$, standard deviation $\sigma_n$, and let \[ P_n(z) = \sum_{k=0}^n \mathbb{P}( X_n = k) z^k ,\] be its probabilityExpand
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Central limit theorems and the geometry of polynomials
Let $X \in \{0,\ldots,n \}$ be a random variable, with mean $\mu$ and standard deviation $\sigma$ and let \[f_X(z) = \sum_{k} \mathbb{P}(X = k) z^k, \] be its probability generating function.Expand
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