Name: Solutions of linear equations in pseudorandom sets
Creator: Ortega Sánchez-Colomer, Miquel
Keywords: :05 Combinatorics::05D Extremal combinatorics [Classificació AMS], Combinatorial analysis, Combinacions (Matemàtica), Combinatorics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria, Classificació AMS::05 Combinatorics::05D Extremal combinatorics, :Matemàtiques i estadística::Matemàtica discreta::Combinatòria [Àrees temàtiques de la UPC], Pseudorandomness, Transference

descriptionPublicationkeyboard_double_arrow_right Master thesis 01 Jan 2022 English Publisher:Universitat Politècnica de Catalunya

Authors: Ortega Sánchez-Colomer, Miquel;

handle: 2117/364896

Solutions of linear equations in pseudorandom sets

- Summary
- Subjects
- Metrics

Abstract

A common theme in modern combinatorics consists in proving sparse analogues of results known in the dense setting. We review some of these for linear systems of equations. We first prove sparse analogues for random sets of Szemerédi s theorem and Rado s theorem via the hypergraph container method. Finally, we prove a sparse analogue for quasirandom sets of Roth s theorem via the regularity method.

Related Organizations

Keywords

:05 Combinatorics::05D Extremal combinatorics [Classificació AMS], Combinatorial analysis, Combinacions (Matemàtica), Combinatorics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria, Classificació AMS::05 Combinatorics::05D Extremal combinatorics, :Matemàtiques i estadística::Matemàtica discreta::Combinatòria [Àrees temàtiques de la UPC], Pseudorandomness, Transference

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average

Usage byUsageCounts

visibility	views	60
download	downloads	83

60
views
83
downloads
Powered by

Found an issue? Give us feedback

visibility

download

Average

Green