Student seminar on the combinatorics of permutations (HS15, Fridays, 1pm in Y27H12)

Planning:

• Sep. 18th: Introduction. Assigning students to presentations.
• Sep. 25th: Descents [Bó, Chapter 1.1] (Vladica Orlovic).
• Oct. 2nd: Alternating runs, alternating permutations and inversions [Bó, Chapters 1.2, 1.3 and 2] (Len Bo Frei and Andreas Pfenninger).
• Oct. 9th: no seminar.
• Oct. 16th: Cycle decomposition [Bó, Chapter 3, without 3.2.6] (Gideon Villiger and Anna Zehnder).
• Oct. 23rd: Pattern avoidance I [Bó, Chapter 4 without 4.4 & Va, Section 2] (Chantal Strasser and Andrea Ritzmann).
• Oct. 30th: Pattern avoidance II [Bó, Chapter 5] (Laura Heimgartner and Pierre Häberli).
• Nov. 6th: On random permutations [Bó, Sections 6.2-6.3 & Wo & Ha] (Helena Noser and Claudia Graf).
• Nov. 13th: Longest increasing subsequence [Ro, Sections 1.1-1.10] (Kathrin Christen and Anja Fallegger).
• Nov. 20th: Enumeration of restricted permutations with inclusion-exclusion [St1, Sections 2.1-2.4] (Silvio Frischnecht) and Posets and simplicial complexes [Bó, Chapter 7.2-7.3] (Mariya Stamatova).
• Nov. 27th: Link with algorithmics [Bó, Chapter 8] (Aline Schillig and Nicolas Himmelsprach).
• Dec. 4th: Link with genomics [Bó, Chapter 9] (Nina Benisowitsch and Sara Carrilho).
• Dec. 11th: Walks in graphs [St2, Chapters 1-4] (Nao Awai and Julia Rauchenstein).
• Dec. 18th: Calculus of tableaux [Fu, Chapters 1-3] (Ralph Gischard and Samuel Noll).

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.