Matches in SemOpenAlex for { <https://semopenalex.org/work/W2250110183> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W2250110183 abstract "We extend various fundamental combinatorial theoremsand techniques from the dense setting to the sparse setting. First,we consider Szemeredi regularity lemma, a fundamental tool inextremal combinatorics. The regularity method, in its originalform, is effective only for dense graphs. It has been a longstanding problem to extend the regularity method to sparse graphs.We solve this problem by proving a so-called counting lemma,thereby allowing us to apply the regularity method to relativelydense subgraphs of sparse pseudorandom graphs. Next, by extendingthese ideas to hypergraphs, we obtain a simplification andextension of the key technical ingredient in the proof of thecelebrated Green-Tao theorem, which states that there arearbitrarily long arithmetic progressions in the primes. The keystep, known as a relative Szemeredi theorem, says that any positiveproportion subset of a pseudorandom set of integers contains longarithmetic progressions. We give a simple proof of a strengtheningof the relative Szemeredi theorem, showing that a much weakerpseudorandomness condition is sufficient. Finally, we give a shortsimple proof of a multidimensional Szemeredi theorem in the primes,which states that any positive proportion subset of Pd (where Pdenotes the primes) contains constellations of any given shape.This has been conjectured by Tao and recently proved by Cook,Magyar, and Titichetrakun and independently by Tao andZiegler." @default.
- W2250110183 created "2016-06-24" @default.
- W2250110183 creator A5021133458 @default.
- W2250110183 date "2015-01-01" @default.
- W2250110183 modified "2023-09-24" @default.
- W2250110183 title "Sparse regularity and relative Szemerédi theorems" @default.
- W2250110183 hasPublicationYear "2015" @default.
- W2250110183 type Work @default.
- W2250110183 sameAs 2250110183 @default.
- W2250110183 citedByCount "0" @default.
- W2250110183 crossrefType "dissertation" @default.
- W2250110183 hasAuthorship W2250110183A5021133458 @default.
- W2250110183 hasConcept C111472728 @default.
- W2250110183 hasConcept C11413529 @default.
- W2250110183 hasConcept C114614502 @default.
- W2250110183 hasConcept C118539577 @default.
- W2250110183 hasConcept C118615104 @default.
- W2250110183 hasConcept C130498168 @default.
- W2250110183 hasConcept C13251829 @default.
- W2250110183 hasConcept C132525143 @default.
- W2250110183 hasConcept C138885662 @default.
- W2250110183 hasConcept C140642157 @default.
- W2250110183 hasConcept C18903297 @default.
- W2250110183 hasConcept C19086982 @default.
- W2250110183 hasConcept C203776342 @default.
- W2250110183 hasConcept C2777759810 @default.
- W2250110183 hasConcept C2780586882 @default.
- W2250110183 hasConcept C33923547 @default.
- W2250110183 hasConcept C43517604 @default.
- W2250110183 hasConcept C46757340 @default.
- W2250110183 hasConcept C86803240 @default.
- W2250110183 hasConceptScore W2250110183C111472728 @default.
- W2250110183 hasConceptScore W2250110183C11413529 @default.
- W2250110183 hasConceptScore W2250110183C114614502 @default.
- W2250110183 hasConceptScore W2250110183C118539577 @default.
- W2250110183 hasConceptScore W2250110183C118615104 @default.
- W2250110183 hasConceptScore W2250110183C130498168 @default.
- W2250110183 hasConceptScore W2250110183C13251829 @default.
- W2250110183 hasConceptScore W2250110183C132525143 @default.
- W2250110183 hasConceptScore W2250110183C138885662 @default.
- W2250110183 hasConceptScore W2250110183C140642157 @default.
- W2250110183 hasConceptScore W2250110183C18903297 @default.
- W2250110183 hasConceptScore W2250110183C19086982 @default.
- W2250110183 hasConceptScore W2250110183C203776342 @default.
- W2250110183 hasConceptScore W2250110183C2777759810 @default.
- W2250110183 hasConceptScore W2250110183C2780586882 @default.
- W2250110183 hasConceptScore W2250110183C33923547 @default.
- W2250110183 hasConceptScore W2250110183C43517604 @default.
- W2250110183 hasConceptScore W2250110183C46757340 @default.
- W2250110183 hasConceptScore W2250110183C86803240 @default.
- W2250110183 hasLocation W22501101831 @default.
- W2250110183 hasOpenAccess W2250110183 @default.
- W2250110183 hasPrimaryLocation W22501101831 @default.
- W2250110183 hasRelatedWork W115873615 @default.
- W2250110183 hasRelatedWork W1497518670 @default.
- W2250110183 hasRelatedWork W1899808675 @default.
- W2250110183 hasRelatedWork W1995043396 @default.
- W2250110183 hasRelatedWork W2068571612 @default.
- W2250110183 hasRelatedWork W2147989485 @default.
- W2250110183 hasRelatedWork W2152535969 @default.
- W2250110183 hasRelatedWork W2153710291 @default.
- W2250110183 hasRelatedWork W2159063988 @default.
- W2250110183 hasRelatedWork W2159703794 @default.
- W2250110183 hasRelatedWork W2290305099 @default.
- W2250110183 hasRelatedWork W2735923117 @default.
- W2250110183 hasRelatedWork W2794535202 @default.
- W2250110183 hasRelatedWork W2963186189 @default.
- W2250110183 hasRelatedWork W3044638218 @default.
- W2250110183 hasRelatedWork W3099496634 @default.
- W2250110183 hasRelatedWork W3168772390 @default.
- W2250110183 hasRelatedWork W603387139 @default.
- W2250110183 hasRelatedWork W912003938 @default.
- W2250110183 isParatext "false" @default.
- W2250110183 isRetracted "false" @default.
- W2250110183 magId "2250110183" @default.
- W2250110183 workType "dissertation" @default.