Linear Structures and Combinatorics

Recommended Prerequisites

Not applicable.

Teaching Methods

Lectures have an expository character, being up to the professor the choice of the most appropriate way to do it and the degree of participation of the students. As an integral part of the learning process, it may be recommended or required  the solution of exercises, course projects or oral presentations.

Learning Outcomes

To familiarize students with concepts, methods and properties pertaining to general counting techniques and to Combinatorics in broad sense.

Work Placement(s)

No

Syllabus

In this course, different ways to approach Combinatorics - either in itself or in association with different algebraic structures - are considered, namely in the fields of Algebraic Combinatorics (in relation with symmetrical functions and group representations or with Coxeter groups), of Enumerative Combinatorics, or of the Combinatorial Theory of Matrices.

Assessment Methods

Assessment
Resolution Problems: 50.0%
Exam: 50.0%

Bibliography

M.Aigner,A Course in Enumeration, Graduate Texts in Mathematics, vol.238, Springer, Berlin,2007

A.Bjorner and F.Brenti,Combinatorics of Coxeter groups, Graduate Texts in Mathematics, vol.231, Springer, Berlin-Heidelberg,2005

W.Fulton,Young Tableaux: with Applications to Representation Theory and Geometry, London Mathematical Society Student Texts, vol. 35, Cambridge University Press, Cambridge,2008

J.Humphreys, Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics, vol. 35,Cambridge University Press,Cambridge,1992

B.E.Sagan, The Symmetric Group. Representations,Combinatorial Algorithms, and Symmetric Functions, Graduate Texts in Mathematics, vol.203,Springer-Verlag, New York,2001

R. Stanley, Enumerative Combinatorics, Volume 1, Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge,1997

R.Stanley,Enumerative Combinatorics, Volume 2,Cambridge Studies in Advanced Mathematics, vol.62, Cambridge University Press, Cambridge,1999.