Selected topics in pigeonholes - NDMI115

• Title: Vybrané kapitoly z holubníků
• Guaranteed by: Department of Applied Mathematics (32-KAM)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2022
• Semester: winter
• E-Credits: 3
• Hours per week, examination: winter s.:2/0, Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: not taught
• Language: Czech, English
• Teaching methods: full-time
• Guarantor: doc. Mgr. Jan Hubička, Ph.D.

Annotation

English

Selected topics from Ramsey theory with special focus on proof techniques of one-dimensional theorem (pigeon hole principles)

Last update: Hubička Jan, doc. Mgr., Ph.D. (28.05.2021)

Czech

Vybraná témata z Ramseyovy teorie se zaměřením na techniky důkazů jednorozměrných vět (principů holubníků)

Last update: Hubička Jan, doc. Mgr., Ph.D. (28.05.2021)

Literature

Graham, Ronald L., Bruce L. Rothschild, and Joel H. Spencer. Ramsey theory. Vol. 20. John Wiley & Sons, 1990.

Prömel, Hans Jürgen. Ramsey theory for discrete structures. Springer Science & Business Media, 2013.

Dodos, Pandelis, and Vassilis Kanellopoulos. Ramsey theory for product spaces. Vol. 212. American Mathematical Soc., 2016.

Todorcevic, Stevo. Introduction to Ramsey spaces (am-174). Vol. 174. Princeton University Press, 2010.

Last update: Hubička Jan, doc. Mgr., Ph.D. (28.05.2021)

Syllabus

English

• pigeon hole principle

• Hales-Jewett theorem

• infinitary extension of the Hales-Jewett theorem (Carlson-Simpson theorem)

• Hindman theorem

• Halpern-Lauchli theorem

Last update: Hubička Jan, doc. Mgr., Ph.D. (28.05.2021)

Czech

• dirichletův princip

• Hales-Jewettova věta

• Nekonečné rozšíření Hales Jewettovy věty (Carlson-Simpsonovo lemma)

• Hindmanova věta

• Halpern-Läuchliho věta

Last update: Hubička Jan, doc. Mgr., Ph.D. (22.09.2021)