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Course, academic year 2018/2019
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Seminar on classification of homogeneous structures - NMAI075
Title in English: Seminář z klasifikace homogenních struktur
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:0/2 C [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: Mgr. Jan Hubička, Ph.D.
Class: DS, diskrétní modely a algoritmy
Informatika Mgr. - volitelný
Classification: Informatics > Discrete Mathematics, Theoretical Computer Science
Mathematics > Discrete Mathematics
Annotation -
Last update: Mgr. Jan Kynčl, Ph.D. (10.05.2018)
A structure is homogeneous if every partial isomorphism extends to an automorphism. For example, every homogeneous graph is thus also edge and vertex transitive. It is intuitively clear that such extremely symmetric structures are rare. The classification programme of homogeneous structures is a project of giving complete catalogs of homogeneous structures of given type (graphs, digraphs, metric spaces etc.)
Literature -
Last update: Mgr. Jan Kynčl, Ph.D. (10.05.2018)

Cherlin, Gregory: Homogeneous Ordered Graphs and Metrically Homogeneous Graphs; Draft of the monograph:

Lachlan, Alistair H., and Robert E. Woodrow. "Countable ultrahomogeneous undirected graphs." Transactions of the American Mathematical Society (1980): 51-94.

Cherlin, Gregory, and Alistair H. Lachlan. "Stable finitely homogeneous structures." Transactions of the American Mathematical Society 296.2 (1986): 815-850.

Cherlin, Gregory L. "Homogeneous directed graphs." Finite and Infinite Combinatorics in Sets and Logic. Springer, Dordrecht, 1993. 81-95.

Syllabus -
Last update: Mgr. Jan Kynčl, Ph.D. (10.05.2018)

In 2018/2019 we will focus on a new monograph by Cherlin, in particular on the chapter on classification of metrically homogeneous graphs.

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