Combinatorics, 2020 Fall, USTC

Instructor:

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

    • Teaching assistants:

  • Jun GAO, email: gj0211@mail.ustc.edu.cn
  • Jialin HE, email: hjxhjl@mail.ustc.edu.cn
  • Tianchi YANG, email: ytc@mail.ustc.edu.cn

    • Syllabus

    Lecture outline will be updated during the semester. [Update: see Combinatorics2020 for a complete collection]

    Week 1

    ** Countings; Binomial Theorem; Estimating.

    Week 2

    ** Inclusion-Exclusion principle; Generating function.

    Week 3

    ** Integer partition, the Catalan number, Randon walk; Exponential Generating function.

    Week 4

    ** Exponential Generating function; Basic of graphs; Sperner's Lemma.

    Week 5

    ** Double counting, Sperner's Theorem, Turan type problems on C4 and K3.

    Week 6

    ** Trees, Cayley's formula (first and second proofs).

    Week 7

    ** Cayley's formula (third proof); Erdos-Ko-Rado Theorem.

    Week 8

    ** Erdos-Ko-Rado Theorem (second proof); Partially ordered set (poset).

    Week 9

    ** Erdos-Szekeres Theorem; Pigeonhole Principle, Ramsey's Theorem.

    Week 10

    ** Ramsey's Theorem, Random graphs.

    Week 11

    ** The Probabilistic Method.

    Week 12

    ** The Probabilistic Method II.

    Week 13

    ** The Probabilistic Method III.

    Week 14

    ** The Algebraic Method.

    Week 15

    ** The Algebraic Method II.

    Week 16

    ** The Algebraic Method III; Finite Projective Plane.

    Week 17

    ** Finite Projective Plane II .

    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

    HW 5 , Tex5

    HW 6 , Tex6

    HW 7 , Tex7

    HW 8 , Tex8

    HW 9 , Tex9

    HW 10, Tex10

    HW 11, Tex11

    HW 12, Tex12