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searching for Counting lemma 10 found (13 total)

Hypergraph regularity method (3,386 words) [view diff] exact match in snippet view article find links to article

combined application of the hypergraph regularity lemma and the associated counting lemma. It is a generalization of the graph regularity method, which refers

Szemerédi regularity lemma (6,159 words) [view diff] case mismatch in snippet view article find links to article

copies of a specific subgraph within the graph up to small error. Graph Counting Lemma. Let H {\displaystyle H} be a graph with V ( H ) = [ k ] {\displaystyle

Roth's theorem on arithmetic progressions (4,444 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle \Lambda (f,g,h)=\sum _{x,y\in \mathbb {Z} }f(x)g(x+y)h(x+2y)} Counting Lemma Let f , g : Z → C {\displaystyle f,g:\mathbb {Z} \rightarrow \mathbb

Hypergraph removal lemma (2,366 words) [view diff] exact match in snippet view article find links to article

regularity lemma (partition hypergraphs into pseudorandom blocks) and a counting lemma (estimate the number of hypergraphs in an appropriate pseudorandom block)

Graphon (5,459 words) [view diff] exact match in snippet view article find links to article

are related more strongly through what are called counting lemmas. Counting Lemma. For any pair of graphons U {\displaystyle U} and W {\displaystyle W}

Extremal graph theory (1,360 words) [view diff] exact match in snippet view article find links to article

of counting lemmas and removal lemmas. In simplest forms, the graph counting lemma uses regularity between pairs of parts in a regular partition to approximate

Pseudorandom graph (2,750 words) [view diff] exact match in snippet view article find links to article

subgraph counting. In addition, the graph counting lemma, a straightforward generalization of the triangle counting lemma, implies that the discrepancy condition

Szemerédi's theorem (2,353 words) [view diff] exact match in snippet view article find links to article

S2CID 18203198. Nagle, Brendan; Rödl, Vojtěch; Schacht, Mathias (2006). "The counting lemma for regular k-uniform hypergraphs". Random Structures Algorithms. 28

Ramsey's theorem (7,887 words) [view diff] exact match in snippet view article find links to article

were obtained since then. In 2013, Conlon, Fox and Zhao showed using a counting lemma for sparse pseudorandom graphs that rind(H) ≤ cn2Δ+8, where the exponent

Cycle index (5,007 words) [view diff] exact match in snippet view article find links to article

Z(G; b, b, ..., b) where b = |Y |. This result follows from the orbit counting lemma (also known as the Not Burnside's lemma, but traditionally called Burnside's