Student seminar on the combinatorics of permutations (FS17, Fridays, 1pm, room Y27H46)

The assistant for the lecture is Jehanne Dousse (Y27H06). She can answer precise questions on your topic, please contact her by e-mail to set an appointment.

On Tuesday before your presentation: you need to send a report (either typed or with a very clean handwriting) on the material that you plan to cover. Please send it by e-mail.

Program of the semester. (It can be adapted depending on the number of interested students.)

Mar. 3rd: Presentation of the seminar and Descents (me) [Bó, Chapter 1.1].
Mar. 10th: Alternating runs, alternating permutations and inversions [Bó, Chapters 1.2, 1.3 and 2] (Noemi Zürcher and Davide Walder).
Mar. 17th: Cycle decomposition [Bó, Chapter 3, without 3.2.6] (Regina Traber and Eleni Winkler).
Mar. 24th: Pattern avoidance I [Bó, Chapter 4 without 4.4 & Va, Section 2] (Jessica Barrifi and Lina Waldburger).
Mar. 31st: Pattern avoidance II [Bó, Chapter 5] (Miranda Hajdini and Marigona Hoti).
Apr. 28th: Longest increasing subsequence [Ro, Sections 1.1-1.10] (Vera Ibrahimi and Stephan Schief).
May 5th: Enumeration of restricted permutations with inclusion-exclusion [St1, Sections 2.1-2.4] (Dimitria Brempou) and Posets and simplicial complexes [Bó, Chapter 7.2-7.3] (Bola Yoon).
May 12th: Link with algorithmics [Bó, Chapter 8] (Petra Brennwald and Carmen Christen).
May 19th: Link with genomics [Bó, Chapter 9] (Simon Gruening and Zouhair Ouaggag).
May 26th: Walks in graphs [St2, Chapters 1-4] (Thomas Läubli and Daniel Siegenthaler).

References:

[Bó] Combinatorics of Permutations, Second Edition, Miklós Bóna, Chapman and Hall/CRC 2012. (available here from UZH server)

[Fu] Young tableaux, William Fulton, London Mathematical Society, Student Texts 35, Cambridge University Press, 1997. (You can borrow the book from me.)

[Ha] Stirling Behavior is Asymptotically Normal, L. H. Harper, Ann. Math. Statist. Volume 38, Number 2 (1967), 410-414. Available here.

[Ro] The Surprising Mathematics of Longest Increasing Subsequences, Dan Romik, Cambridge University Press, 2015. Available here.

[St1] Enumerative Combinatorics, Volume 1, Richard Stanley, Cambridge Studies in Advanced Mathematics 49, Cambridge University Press, Second Edition, 2012. (You can borrow the book from me.)

[St2] Algebraic Combinatorics: Walks, Trees, Tableaux, and More, Richard Stanley, Undergraduate Texts in Mathematics, Springer, 2013. Available here.

[Va] Permutation classes, Vincent Vatter, arXiv:1409.5159,

[Wo] Note on Runs of Consecutive Elements, J. Wolfowitz, Ann. Math. Statist., Volume 15, Number 1 (1944), 97-98. Available here.