Results 41 to 50 of about 524 (71)
Sharp thresholds for Ramsey properties
Forum of Mathematics, SigmaIn this work, we develop a unified framework for establishing sharp threshold results for various Ramsey properties. To achieve this, we view such properties as noncolourability of auxiliary hypergraphs.
Ehud Friedgut +3 more
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, 2009 This expository paper discusses some conjectures related to visibility and blockers for sets of points in the ...
Pór, Attila, Wood, David R.
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Generalized Ramsey–Turán density for cliques
Forum of Mathematics, SigmaWe study the generalized Ramsey–Turán function $\mathrm {RT}(n,K_s,K_t,o(n))$ , which is the maximum possible number of copies of $K_s$ in an n-vertex $K_t$ -free graph with independence number $o(n)$ . The case when $s=2$
Jun Gao +3 more
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Block sizes in the block sets conjecture
Forum of Mathematics, SigmaA set X is called Euclidean Ramsey if, for any k and sufficiently large n, every k-colouring of $\mathbb {R}^n$ contains a monochromatic congruent copy of X.
Maria-Romina Ivan +2 more
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IP$^{*}$-sets in function field and mixing properties
, 2017 The ring of polynomial over a finite field $F_q[x]$ has received much attention, both from a combinatorial viewpoint as in regards to its action on measurable dynamical systems.
De, Dibyendu, Debnath, Pintu
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Forbidden induced subgraphs for graphs and signed graphs with eigenvalues bounded from below
Forum of Mathematics, SigmaThe smallest eigenvalue of a graph is the smallest eigenvalue of its adjacency matrix. We show that the family of graphs with smallest eigenvalue at least $-\lambda $ can be defined by a finite set of forbidden induced subgraphs if and only if
Zilin Jiang, Alexandr Polyanskii
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Irrational numbers associated to sequences without geometric progressions [PDF]
, 2013 Let s and k be integers with s \geq 2 and k \geq 2. Let g_k^{(s)}(n) denote the cardinality of the largest subset of the set {1,2,..., n} that contains no geometric progression of length k whose common ratio is a power of s.
Nathanson, Melvyn B., O'Bryant, Kevin
core
On Ramsey numbers of complete graphs with dropped stars
, 2016 Let $r(G,H)$ be the smallest integer $N$ such that for any $2$-coloring (say, red and blue) of the edges of $K\_n$, $n\geqslant N$, there is either a red copy of $G$ or a blue copy of $H$.
Alfonsín, Jorge Ramírez +2 more
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Asymmetric infinite sumsets in large sets of integers
Forum of Mathematics, SigmaWe show that for any set $A\subset {\mathbb N}$ with positive upper density and any $\ell ,m \in {\mathbb N}$ , there exist an infinite set $B\subset {\mathbb N}$ and some $t\in {\mathbb N}$ so that $\{mb_1 + \ell b_2 ...
Ioannis Kousek
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Partition regularity of Pythagorean pairs
Forum of Mathematics, PiWe address a core partition regularity problem in Ramsey theory by proving that every finite coloring of the positive integers contains monochromatic Pythagorean pairs (i.e., $x,y\in {\mathbb N}$ such that $x^2\pm y^2=z^2$ for some $z ...
Nikos Frantzikinakis +2 more
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