**Where and when:** Tuesdays at 13:15-15:00 in room 3733.

**Instructor:** Petter Brändén, room 3626

**Credits: **7.5, **Grades: **A-F, **Language: **English

**Literature:** R. P. Stanley, Enumerative Combinatorics, second edition, Cambridge University Press, 2011 (Electronic copy available at Stanley's homepage).

**Contents: **Basic methods in enumerative combinatorics. Sieve methods, for example inclusion-exclusion, the involution principle and the method of using determinants to count lattice paths. Various aspects of the theory of partially ordered sets, for example lattice theory, Möbius inversion in posets, P-partitions, and connections to topology.

**Examination and grading: **Four sets of homework problems will be handed out. Here is how the grading works:

*Undergraduate students*: Solving roughly 85% of the problems gives grade B, 75% gives C, 65% gives D, 55% & gives E, 50% gives Fx. In addition, one can choose to do a voluntary assignment which consists of writing a summary of a research article. Details about this assignment and articles to choose from can be found here. If satisfactory written, the summary will raise one's grade by one step.

*Graduate students*: In order to pass, one must solve 70% of the homework problems and hand in a satisfactory summary of a research article.

**Homework:** Collaboration is allowed, but you should write the solutions yourself. Please show all your work!

**HW1.** (To be handed in Feb. 28): Exercises from Stanley 1: 1.12 (Hint: Use Euler's formula for planar graphs), 1.20, 1.26, 1.33a, 44a, 47ab, 102abc, 114ab, 121ab.

**HW2. ** (To be handed in March 20): PDF

**HW3. ** (To be handed in April 17): PDF

**HW4. ** (To be handed in May 22): PDF

**Schedule: **

Date | Plan |
---|---|

01-19 | Ch. 1.1-1.2. |

01-24 | Ch. 1.1-1.3. |

01-31 | Ch. 1.3-1.4. |

02-07 | Ch. 1.7-1.9, 2.1-2.2. |

02-14 | Ch. 2.1-2.2, 2.7 |

02-21 | NO CLASS! |

02-27 | Ch. 2.7, 3.1-3.2 |

03-06 | Ch. 3.2-3.4 |

03-13 | Ch. 3.4-3.8 |

03-20 | Ch. 3.8-3.11 |

03-27 | Ch. 3.11 |

04-03 | NO CLASS! |

04-10 | Ch. 3.11, Ch. 3.15. Notes from class: PDF. Exposition differs slightly from book. |

04-17 | Ch. 3.15, 3.12, 3.13 |

05-01 | NO CLASS! Public Holidays |