Combinatorics, 2016 Fall, USTC

Instructor:

  • Jie Ma, Email: jiema@ustc.edu.cn, Office: 1603, School of Math

    • Teaching assistants:

  • Ling QIN, email: ql5972@mail.ustc.edu.cn, phone: 152-5691-7315
  • Xiao TAN, emial: xiaotan@mail.ustc.edu.cn, phone: 152-5607-7990
  • Xiaofan YUAN, email: yxf518@mail.ustc.edu.cn, phone: 156-5609-6490

    • Syllabus

    Lecture outline will be updated during the semester

    Week 1

    ** Countings; Binomial Theorem; Estimating.

    Week 2

    ** Inclusion¨CExclusion principle.

    Week 3

    ** Generating function and its applications, including integer partition and Catalan number.

    Week 4

    ** Random walk; Exponential generating function.

    Week 5

    ** Baisc of graphs.

    Week 6

    ** Spener's Lemma (a planar version)£» Double counting, including Sperner's Theorem.

    Week 7

    ** Turan type problems (an upper bound on ex(n, C4) and Mantel's Theorem); Tree and Cayley¡¯s Formula (1st proof).

    Week 8

    ** Cayley's Formula (2nd and 3rd proofs); Erdos-Ko-Rado Theorem (1st proof).

    Week 9

    ** Erdos-Ko-Rado Theorem (2nd proof).

    Week 10

    ** Partially ordered sets.

    Week 11

    ** The Pigeonhole Principle; Ramsey's Theorem

    Week 12

    ** Ramsey's Theorem (continued).

    Week 13

    ** The Probabilistic Method.

    Week 14

    ** The Probabilistic Method (continued).

    Week 15

    ** The linear algebraic Method.

    Week 16

    ** The linear algebraic Method (continued).

    Homeworks:

    HW 1 . If you want to use the tex file of the problem set, download Tex1

    HW 2 , Tex2

    HW 3 , Tex3

    HW 4 , Tex4 Problem 7 has been updated.

    HW 5 , Tex5

    HW 6 , Tex6

    HW 7 , Tex7

    HW 8 , Tex8

    HW 9 , Tex9

    HW 10 , Tex10

    HW 11 , Tex11

    HW 12 , Tex12

    HW 13 , Tex13