KIAS Workshop on Combinatorics

The "KIAS Workshop on Combinatorics" will be held at KIAS, Seoul on May 30- June 1, 2013. If you want to participate, please write a registration form and email to kias@combinatorics.kr until May 10. This workshop will be supported by Open KIAS.

Information

• • Title KIAS Workshop on Combinatorics

• Date May 30 - June 1 (Thu-Sat), 2013

• Venue Room 1503, KIAS

• Web http://kias.combinatorics.kr

• Organizers

  • Jeong Han Kim, KIAS

  • Boram Park, NIMS

• Program Committee

  • Seog-Jin Kim, Konkuk University

  • Youngsoo Kwon, Yeungnam University

  • Seunghyun Seo, Kangwon National University

  • Heesung Shin, Inha University

• Invited Speakers

  • Gi-Sang Cheon, Sungkyunkwan University

  • Jeong Ok Choi. GIST

  • Mitsugu Hirasaka, Pusan National University

  • Hyun Kwang Kim, POSTECH

  • Sangwook Kim, Chonnam National University

  • Seog-Jin Kim, Konkuk University

  • Younjin Kim, KAIST

  • Youngsoo Kwon, Yeungnam University

  • Seunghyun Seo, Kangwon National University

  • Hwanchul Yoo, KIAS

• We are going to

  • give 10 invited talks without contributed talks.

  • provide for 5 meals (dinner of May 30, breakfast, lunch, & dinner of May 31, breakfast of June 1) of all participates.

  • support the accommodation for two nights of all students who register until April 30.

Talks (Abstract)

• • Session A

    • Chairman Seog-Jin Kim, Konkuk University

    • Talk 1

      • Speaker Gi-Sang Cheon, Sungkyunkwan University

      • Title The Riordan group and related topics in Combinatorics and Matrix Theory

      • Abstract The Riordan group is the set of infinite lower triangular matrices whose kth column has the generating function g(z)f(z)^k where g and f are elements of the ring of formal power series C[[z]] such that g(0)=1, f(0)=0 and f'(0)<>0. Such a matrix is called Riordan matrix and denoted as (g(z); f(z)) or (g; f). The Riordan group shows up naturally in a variety of combinatorial settings and combinatorial matrix theory. This talk is given by two parts. The concept of Riordan group and Riordan matrix will be introduced in the first part by presenting fundamental properties and interesting subgroups. In the second part, we discuss how this concept can be applied to several problems arising in combinatorics and matrix theory.

    • Talk 2

      • Speaker Seog-Jin Kim, Konkuk University

      • Title Coloring of the square of Kneser graphs

      • Abstract The Kneser graph K(n,k) is the graph whose vertices are the k-elements subsets of an n-element set, with two vertices adjacent if the sets are disjoint. The square G² of a graph G is the graph defined on V(G) such that two vertices u and v are adjacent in G² if the distance between u and v in G is at most 2. We denote the square of the Kneser graph K(n,k) by K²(n,k). The problem of computing χ(K²(n,k)), which was originally posed by Füredi, was introduced and discussed by Kim and Nakprasit (2004). Note that that A and B are adjacent in K²(n,k) if and only if A∩B=∅ or |A∩B|≧3k-n. Therefore, K²(n,k) is the complete graph K_t where t=_nC_k if n≧3k-1, and K²(n,k) is a perfect matching if n=2k. But for 2k+1≦n≦3k-2, the exact value of χ(K²(n,k)) is not known. Hence it is an interesting problem to determine the chromatic number of the square of the Kneser graph K(2k+1,k) as the first nontrivial case. We will give a brief introduction of the problem, and present recent results. This talk is based on joint work with Boram Park.

    • Talk 3

      • Speaker Hyun Kwang Kim, POSTECH

      • Title Polytope numbers and their applications

      • Abstract These is an introductory lecture on combinatorial properties of polytope numbers. We first introduce polytope numbers and their basic properties such as product formula and decomposition theorems. Next we illustrate these properties with some well-known polytopes. Finally we give research problems related to polytope numbers.

  • Session B

    • Chairman Youngsoo Kwon, Yeungnam University

    • Talk 4

      • Speaker Jeong Ok Choi, GIST

      • Title Fractional weak discrepancy of posets

      • Abstract In this talk, various discrepancies of posets (Partially Ordered Sets) will be introduced. In particular, fractional weak discrepancy of a poset is emphasized as a refinement of measuring weakness of a poset. We characterize forbidden structure for posets preventing fractional weak discrepancy larger than k for each natural number k. Also, we give the range of fractional weak discrepancy of (M;2)-free posets.

    • Talk 5

      • Speaker Mitsugu Hirasaka, Pusan National University

      • Title Zeta functions of adjacency algebras of association schemes

      • Abstrac For a module L which has only finitely many submodules with a given finite index we define the zeta function of L to be a formal Dirichlet series ζ_L(s)=∑_n≥1 a_n n^-s where a_n is the number of submodules of L with index n. For a commutative ring R and an association scheme (X,S) we denote the adjacency algebra of (X,S) over R by RS. In this talk we aim to compute ζ_ZS(s) under several assumptions where ZS is viewed as a regular ZS-module.

  • Session C

    • Chairman Heesung Shin, Inha University

    • Talk 6

      • Speaker Youngsoo Kwon, Yeungnam University

      • Title Classification of regular embeddings of some graph families

      • Abstract A regular embedding is a highly symmetric graph embedding onto a surface. Classifications of regular embeddings are pursued by three different directions: by given graphs, groups and surfaces. In this talk, we will consider classification of regular embeddings of graphs. I will introduce several methods to classify regular embeddings of graphs and some recent results.

    • Talk 7

      • Speaker Seunghyun Seo, Kangwon National University

      • Title Colored permutations and generalizations of derangements

      • Abstract A derangement is a permutation without any fixed points. There are several generalizations of derangements in the literature. In this talk, we introduce 5 types of colored permutations which are all generalizations of derangements. We present the generating function of each type and find the hierarchy of them combinatorially. We also present bijective proofs among the objects. This is joint work with Dongsu Kim(NIMS) and Jang Soo Kim(KIAS).

    • Talk 8

      • Speaker Hwanchul Yoo, KIAS

      • Title Balanced labellings of affine permutations and symmetric functions

      • Abstract In this talk, we introduce a generalization of the balanced labellings of Fomin, Greene, Reiner, and Shimozono. We extend the notion in two directions: (1) we define the diagrams of affine permutations and the balanced labellings on them; (2) we define the set-valued version of the balanced labellings. We show that the column-strict balanced labellings on the diagram of an affine permutation yield the affine Stanley symmetric function defined by Lam, and that the column-strict set-valued balanced labellings yield the affine stable Grothendieck polynomial of Lam. Moreover, once we impose suitable flag conditions, the flagged column-strict set-valued balanced labellings on the diagram of a finite permutation give a monomial expansion of the Grothendieck polynomial of Lascoux and Schutzenberger. We also give a necessary and sufficient condition for a diagram to be an affine permutation diagram.

  • Session D

    • Chairman Seunghyun Seo, Kangwon National University

    • Talk 9

      • Speaker Sangwook Kim, Chonnam National University

      • Title Flag enumeration of matroid base polytopes

      • Abstract For a matroid on [n], a matroid base polytope is the polytope in Rⁿ whose vertices are the incidence vectors of the bases of the matroid. In this talk, we discuss flag information of matroid base polytopes for some classes of matroids such as rank 2 matroids and lattice path matroids

    • Talk 10

      • Speaker Younjin Kim, KAIST

      • Title On Combinatorial problems of Erdös

      • Abstract For a property Γ and a family of sets F, let f(F,Γ) be the size of the largest subfamily of F having property Γ. For a positive integer m, let f(m,Γ) be the minimum of f(F,Γ) over all families of size m. In 1972, Erdös and Shelah also considered Γ to be the property that no four distinct sets satisfy F₁∩F₂=F₃ and F₁∩F₂=F₄. Such families are called B₂-free. Erdös and Shelah gave an example showing f(m,B₂-free)≦(3/2)m^2/3 and they also conjectured f(m,B₂-free)>c₂m^2/3. We verify a conjecture of Erdös and Shelah from 1972. In1964, Erdös, Hajnal, and Moon introduced the following problem: get the minimum size of a graph G such that G does not contain F as a subgraph but the addition of any new edge creates at least one copy of F in G. This minimum is called the saturation number of F. We obtain the saturation number of C_k, where C_k is a cycle with length k.

Banquet (Dinner of May 31)

• • 장소는 홀리데이인 성북 호텔 (http://www.holiday.co.kr/holiday/) 뷔페 입니다.

• 호텔측에서 준비한 차량으로 이동할 예정입니다. (5:30분 고등과학원앞)

Registration

• If you want to participate, please fill out the registration form at the bottom of this page and email to kias@combinatorics.kr until May 10, 2013.

• We plan to reserve hotels near KIAS for participants who register before April 30.

• We are going to support the accommodation of graduate students who registered on before April 30.

• We encourage students to come to the workshop.

Participants