M502 Combinatorics~II, Spring 2006
M502 Combinatorics II, Spring 2006
Dr. A. Betten, room 207, Weber building
When and where
M W F 2:10 - 3:00 ENGRG E106
van Lint / Wilson: Combinatorics, Cambridge
M501 would be nice but this time we open it up to everybody!
(I'll give you a brief review in the beginning anyway)
M502 is the second course in a 1-year's sequence of graduate intoductory combinatorics.
The goal is to show how basic structures can be attacked with combinatorial methods.
This will give the student an understanding of the methods with which
discrete structures are explored, constructed and classified.
The border to actual research is not very far from where we will be.
- Algebraic graph theory (eigenvalues, Bose-Mesner algebra,
special classes of graphs and digraphs etc)
Isomorph free exhaustive generation of graphs and other discrete structures
using the method of canonical forms and partition backtracking.
Hadamard matrices (construction methods, the new Hadamard matrix of order 428
constructed by Kharagani and Tayfeh-Rezaie in 2005)
Error correcting codes, parameter, bounds, classes of codes, weights, duality,
Reed-Muller, BCH and Reed-Solomon codes,
codes from curves.
Projective spaces, in particular finite projective planes,
Desargues, Pappus, coordinates, Latin squares, collineations.
Ovals in Desarguesian projective planes, their Combinatorics,
new construction methods using geometric codes.
Combinatorics of tableaux, the hook formula, symmetric polynomials
(elementary, monomial, complete, forgotten, power, Schur) and their Combinatorics.
Characters of Sn.
Designs, Steiner systems, parameter, standard constructions, square designs,
construction with prescribed automorphism group, codes and designs.
Linear Spaces, in particular the recent theory of line transitive
point imprimitive ones, their Combinatorics and how to generate them.
Extremal Combinatorics: distinct representatives (Hall), Ramsey, Sperner, Erdos etc.
Class participation and homework are essential, as is the final exam.
I expect that course participants present small subject topics
towards the end of the semester.
The mix is: final / subject topic presentation / homework / class participation
as to 30 / 30 / 30 / 10.
For further information
Please contact A. Betten:
or visit the course webpage at
File translated from
On 18 Jan 2006, 11:12.