Enumerative Combinatorics

This subject is not offered in 2013.

3 contact hours and 7 hours private study per week.

The following, or equivalent.

None

Use of mathematical symbolic computation packages such as Mathematica and Maple is encouraged.

None

For the purposes of considering requests for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements for this entry.

The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/

The subject is about the use of generating functions for enumeration of combinatorial structures, including partitions of numbers, partitions of sets, permutations with restricted cycle structure, connected graphs, and other types of graph. The subject covers the solution of recurrence relations, methods of asymptotic enumeration, and some applications in statistical mechanics. The methods covered have widespread applicability, including in areas of pure and applied mathematics and computer science.

After completing this subject, students should

• have learned about the use of generating functions for enumeration of combinatorial structures, including partitions of numbers and of sets, permutations with restricted cycle structure, connected graphs and other types of graph;
• have studied the solution of recurrence relations; methods of asymptotic enumeration;
• have considered some applications in statistical mechanics;
• gain the ability to pursue further studies in this and related areas.

Up to 50 pages of written assignments (40%: two assignments worth 20% each, due mid and late in semester), a 3 hour written examination (60%, in the examination period).

"Analytic Combinatorics" by Philippe Flajolet and Robert Sedgewick, Cambridge University Press, 2009

None

This subject is not available as a breadth subject.

Upon completion of this subject, students should gain the following generic skills:

• Problem-solving skills including the ability to engage with unfamiliar problems and identify relevant solution strategies;
• Analytical skills through the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis; and
• Time management skills: the ability to meet regular deadlines while balancing competing commitments.