Math 274: Combinatorics II
(Graduate combinatorics, 2nd semester)
|Instructor:||Sam Hopkins (call me "Sam")|
|Office: Academic Support Bldg B - 214 (temporary)
|Course format:||Online (via Zoom: link will be emailed)|
|Office hours:||By appointment (email me to set up a time)|
|Course content:||This is the 2nd semester of graduate combinatorics (click here for the 1st semester).|
| We will continue to study the enumeration of discrete structures, with a new focus on connections to algebra (a.k.a. symmetries!). We will try to cover the following:
|Prerequisites:||Calculus, linear algebra, undergraduate algebra (groups, rings, fields).|
|It's helpful to have taken the 1st semester of grad combinatorics, but is not strictly necessary.|
|Main text:||B. Sagan, Combinatorics: the Art of Counting.|
|In the 1st semester we covered material from Chapters 1-5 (even though this was not the main text for that course). In this semester we will study material from Chapters 6 and 7.|
|Other nice sources:||(for group actions) L. Shapiro, Finite Groups Acting on Sets with Applications.|
| (for symmetric functions) B. Sagan, The Symmetric Group.
(for both topics) Chapter 7 of R.P. Stanley, Enumerative combinatorics, Vol. II.
(for the "toggle" description of RSK) S. Hopkins, RSK via local transformations.
|Class notes:||Batch 1; Batch 2; Batch 3; Batch 4; Batch 5; Batch 6; Batch 7; Batch 8|
|Grading:||There will be 3 homework assignments for the semester.|
|The grading of the assignments will depend on both the quality and quantity of homework turned in. Beyond that, I expect you to show up to class and be engaged. Collaboration on the homework is encouraged, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework page with whom they collaborated.|
|Homework assignments:||I will write the problems myself, possibly adapting Sagan's exercises.|