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250157 VU Selected Topics in Combinatorics (2026W)
Prüfungsimmanente Lehrveranstaltung
Labels
An/Abmeldung
Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").
- Anmeldung von Di 01.09.2026 00:00 bis Mo 21.09.2026 23:59
- Abmeldung bis Sa 31.10.2026 23:59
Details
max. 25 Teilnehmer*innen
Sprache: Englisch
Lehrende
Termine (iCal) - nächster Termin ist mit N markiert
- Donnerstag 01.10. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- N Mittwoch 07.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 08.10. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 14.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 15.10. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 21.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 22.10. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 28.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 29.10. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 04.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 05.11. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 11.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 12.11. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 18.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 19.11. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 25.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 26.11. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 02.12. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 03.12. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 09.12. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 10.12. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 16.12. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 17.12. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 07.01. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 13.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 14.01. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 20.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 21.01. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 27.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 28.01. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Information
Ziele, Inhalte und Methode der Lehrveranstaltung
The course introduces selected advanced topics in enumerative and algebraic combinatorics, with particular emphasis on the interplay between combinatorial structures, generating functions, special functions, and algebraic methods.Topics are expected to include q-enumeration and basic hypergeometric series, partitions and q-binomial coefficients, weighted lattice paths and nonintersecting path methods, rook theory and q-rook theory, as well as selected multivariate and elliptic extensions. Connections with tableaux, symmetric functions, and combinatorial representation theory will be discussed where appropriate. Depending on the progress of the course and the interests of the participants, further related topics of current research may be included.A recurring theme will be the passage between algebraic identities and combinatorial models. Generating-function and hypergeometric identities will be studied together with interpretations in terms of lattice paths, rook placements, partitions, tableaux, and related structures. The later parts of the course will provide an introduction to selected topics close to current research.The course combines lectures with guided problem solving, regular homework assignments, and independent project work. Students will carry out a small project on a selected topic related to the course and present the main ideas and results in a short presentation. The project component is intended to develop experience in reading advanced mathematical literature, identifying the essential structure of an argument, and communicating mathematics clearly.No prior knowledge of q-series, hypergeometric series, elliptic functions, symmetric functions, or representation theory is assumed. The necessary concepts will be introduced as needed. A solid background in undergraduate mathematics, including basic combinatorics, linear algebra, and generating functions, is expected.
Art der Leistungskontrolle und erlaubte Hilfsmittel
Assessment is continuous and consists of four components:*) regular homework assignments: 40%;
*) an individual or, where appropriate, small-group student project: 25%;
*) a short presentation based on the project: 15%;
*) a concluding individual oral assessment: 20%.Homework assignments will include both routine exercises and more substantial proof problems. Selected problems may be discussed or presented in class.The student project will consist of a written component and an oral presentation.The written component, which counts for 25% of the final grade, will normally take the form of a concise mathematical handout or short report on a selected topic related to the course. It should present the main definitions, ideas, results, and references in a form that is understandable and useful to the other participants of the course. Depending on the topic, it may also include worked examples, proof sketches, computations, or a discussion of connections with other material from the course.The oral presentation, which counts for 15% of the final grade, will be based on the same project and should explain the central ideas and results clearly to the class.For homework and projects, students may use the lecture notes, standard reference literature, and other mathematical sources, provided that all submitted work is written independently and all external sources are properly acknowledged. Collaboration in discussing homework problems is encouraged, but each student must prepare and submit their own solutions unless a task is explicitly designated as collaborative.During the oral assessment, no aids are normally required; any exceptions will be announced in advance.
*) an individual or, where appropriate, small-group student project: 25%;
*) a short presentation based on the project: 15%;
*) a concluding individual oral assessment: 20%.Homework assignments will include both routine exercises and more substantial proof problems. Selected problems may be discussed or presented in class.The student project will consist of a written component and an oral presentation.The written component, which counts for 25% of the final grade, will normally take the form of a concise mathematical handout or short report on a selected topic related to the course. It should present the main definitions, ideas, results, and references in a form that is understandable and useful to the other participants of the course. Depending on the topic, it may also include worked examples, proof sketches, computations, or a discussion of connections with other material from the course.The oral presentation, which counts for 15% of the final grade, will be based on the same project and should explain the central ideas and results clearly to the class.For homework and projects, students may use the lecture notes, standard reference literature, and other mathematical sources, provided that all submitted work is written independently and all external sources are properly acknowledged. Collaboration in discussing homework problems is encouraged, but each student must prepare and submit their own solutions unless a task is explicitly designated as collaborative.During the oral assessment, no aids are normally required; any exceptions will be announced in advance.
Mindestanforderungen und Beurteilungsmaßstab
Because this is a course with continuous assessment, regular participation in the exercise component, regular submission of homework, completion of the student project, participation in the project presentation, and participation in the concluding oral assessment are required.To obtain a positive grade, students must achieve an overall positive performance and must demonstrate adequate understanding of the central concepts and methods of the course. In addition, the student project and the concluding oral assessment must each be completed at a satisfactory level.The final grade is determined as follows:*) homework assignments: 40%;
*) student project: 25%;
*) short project presentation: 15%;
*) concluding individual oral assessment: 20%.Assessment will take into account mathematical correctness, quality of reasoning, conceptual understanding, clarity of written and oral exposition, and the ability to apply methods from the course to related problems.The precise organizational details concerning homework submission, project topics, project format, and presentation dates will be announced at the beginning of the semester.
*) student project: 25%;
*) short project presentation: 15%;
*) concluding individual oral assessment: 20%.Assessment will take into account mathematical correctness, quality of reasoning, conceptual understanding, clarity of written and oral exposition, and the ability to apply methods from the course to related problems.The precise organizational details concerning homework submission, project topics, project format, and presentation dates will be announced at the beginning of the semester.
Prüfungsstoff
The examination material consists of the mathematical concepts, methods, examples, and principal results developed in the course, together with the corresponding material in the lecture notes and exercise sheets.This will include, as covered during the semester, topics such as q-numbers, q-binomial coefficients, q-shifted factorials and elementary q-series; selected basic hypergeometric summations and transformations; weighted combinatorial enumeration and generating-function methods; lattice-path enumeration and nonintersecting lattice paths; determinant methods in combinatorics; classical rook theory and weighted or q-analogues; selected topics involving partitions, tableaux, symmetric functions, or combinatorial representation theory; and introductory multivariate and elliptic extensions of classical and q-combinatorial constructions.The precise scope of the examination material will be determined by the material actually covered in the course. Students will not be expected to know advanced topics or results that were merely mentioned as further directions.For the individual project, students are expected to understand and be able to explain the material that they have studied in greater depth for their chosen project topic.
Literatur
The course will be largely self-contained. Lecture notes and exercise sheets will be made available during the semester. No single textbook covers all topics of the course.Useful references include:G. E. Andrews, R. Askey and R. Roy, Special Functions, Cambridge University Press.G. Gasper and M. Rahman, Basic Hypergeometric Series, 2nd ed., Cambridge University Press.R. P. Stanley, Enumerative Combinatorics, Vol. 1, 2nd ed., Cambridge University Press.R. P. Stanley, Enumerative Combinatorics, Vol. 2, 2nd ed., Cambridge University Press.For individual topics such as lattice-path methods, rook theory, symmetric functions, multivariate and elliptic hypergeometric series, additional articles and expository references will be indicated during the semester.The reading list is intended primarily as a collection of reference works; students are not expected to read these books in their entirety.
Zuordnung im Vorlesungsverzeichnis
ML2; MEL; MALV
Letzte Änderung: Sa 05.09.2026 05:06