Enumerative Combinatorics School 2014

The Enumerative Combinatorics School 2014 (ECS2014) will be held at Center for Applications of Mathematical Principles (CAMP), National Institute for Mathematical Sciences (NIMS), Daejeon on April 4-6, 2014.

The purpose of this school is not just presenting individual works but teaching basic concepts and tools of enumerative combinatorics. So we invite 4 lecturers, each of whom has two 90-minute letures or three 60-minute lectures. All topic of lectures are including "enumeration" of combinatorial objects, and the style of talk tends to be less formal.

In principle, registration is on a first-come, first-served basis. If you want to participate, please write a registration form until March 21.

Information

  • Organizers
    • Seunghyun Seo (Kangwon National University) 
    • Heesung Shin (Inha University)
    • Host National Institute for Mathematical Sciences
    • Sponsor 2014 NIMS School (2014년 개방형 학술교류 프로그램)
    • We are going to 
      • give just six 60-minute lectures and four 90-minute lectures in Korean. 
      • provide for 6 meals (dinner of April 4, breakfast, lunch & dinner of April 5, and breakfast & lunch of April 6) of all participants. 
      • support the accommodation of all participants registered until March 21. (except from Daejeon area) 
      • distribute the abstracts of ECS2014. 

    Invited Lecturers

    • Jang Soo Kim (Sungkyunkwan University) 
    • Sangwook Kim (Chonnam National University) 
    • Boram Park (NIMS) 
    • Seunghyun Seo (Kangwon National University)

      Timetable

      • April 4 (Friday) 
        • 00h00 - 14h00 Registration 
        • 14h00 - 00h00 Opening Ceremony 
        • 14h00 - 15h00 Lecture SS-1 
        • 15h15 - 16h45 Lecture BP-1 
        • 17h00 - 18h00 Lecture SK-1 
        • 18h00 - 00h00 Dinner

      • April 5 (Saturday) 
        • 08h30 - 09h30 Breakfast 
        • 09h30 - 10h30 Lecture SS-2 
        • 10h45 - 12h15 Lecture JK-1 
        • 12h15 - 14h00 Lunch 
        • 14h00 - 15h00 Lecture SK-2 
        • 15h15 - 16h45 Lecture BP-2 
        • 17h00 - 18h00 Lecture SS-3
        • 18h00 - 00h00 Dinner 

      • April 6 (Sunday) 
        • 08h30 - 09h30 Breakfast 
        • 09h30 - 10h30 Lecture SK-3 
        • 10h45 - 12h15 Lecture JK-2 
        • 12h15 - 00h00 Closing Ceremony

      Program

      • Lecture JK-1
        • Speaker Jang Soo Kim (Sungkyunkwan University)
        • Language Korean
        • Length 90 min
        • Title Viennot’s combinatorial theory of orthogonal polynomials
        • Abstract An orthogonal polynomial sequence is a family of polynomials which are orthogonal under an inner product. In this lecture we will study Viennot’s combinatorial theory of orthogonal polynomials.
          We will first start with definitions and basic properties of orthogonal polynomials such as 3-term recurrence relations. We then show that the moment of orthogonal polynomials can be viewed as a generating function for weighted Motzkin paths. We will see that the moments of Hermite, Charlier, and Laguerre polynomials are equal to the numbers of matchings, partitions, and permutations. If time permites, we will also consider q-analogs of these polynomials.
        • Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414546542].wmv
          Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414735322].wmv

      • Lecture JK-2
        • Speaker Jang Soo Kim (Sungkyunkwan University)
        • Language Korean 
        • Length 90 min
        • Title Linearization coefficients
        • Abstract For an orthogonal polynomial sequence, the nth polynomial pn(x) is of degree n. Thus we can always write pn(x)pm(x) as a unique linear sum of these polynomials, i.e.,
          pn(x)pm(x) = ∑l an,m,l pl(x)
          The coefficients an,m,l are called linearization coefficients.
          In the second lecture we will show that the linearization coefficients for Hermite, Charlier Laguerre polynomials are equal to the numbers of inhomogeneous matchings, inhomogeneous partitions, and multi-derangements. If time permites, we will also consider q-analogs of these polynomials.
        • Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414152732].wmv
          Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414865812].wmv

      • Lecture SK-1
        • Speaker Sangwook Kim (Chonnam National University)
        • Language Korean 
        • Length 60 min
        • Title Order complexes and face posets
        • Abstract We begin by defining the order complex of a poset and the face poset of a simplicial complex. These constructions enable us to view posets and simplicial complexes as essentially the same topological object. They link combinatorics with topology and other areas of mathematics in a deep and fundamental way. Combinatorial interest in poset topology dates back to Gian-Carlo Rota’s seminal 1964 paper on the Möbius function of a partially ordered set. The Möbius number of a poset, an important combinatorial invariant, is equal to the reduced Euler characteristic of the order complex, an important topological invariant.
          We will discuss various applications of poset topology in the theory of hyperplane and subspace arrangements. Some connections with graphs, groups and lattices are also discussed.
        • Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414208412].wmv
        • Reference Poset Topology: Tools and Applications, written by Michelle L. Wachs
      • Lecture SK-2
        • Speaker Sangwook Kim (Chonnam National University)
        • Language Korean 
        • Length 60 min
        • Title Shellability and edge labelings
        • Abstract Shellability is a combinatorial property of simplicial and more general cell complexes, with strong topological and algebraic consequences. Shellability first appeared in the middle of the nineteenth century in Schläfli's computation of the Euler characteristic of a convex polytope. The original theory of shellability applied only to pure complexes. In the early 1990's, a nonpure simplicial complex arose in the complexity theory with topological properties somewhat similar to those of pure shellable complexes. This led Björner and Wachs to extend the theory of shellability to nonpure complexes.
          Lexicographic labeling is an labeling of the edges of the Hasse diagram of a poset in a certain way which implies shellability of the order complex of the poset. Two versions of lexicographic shellability, EL-shellability and CL-shellability will be discussed with several examples.
        • Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414738122].wmv
        • Reference Poset Topology: Tools and Applications, written by Michelle L. Wachs

      • Lecture SK-3
        • Speaker Sangwook Kim (Chonnam National University)
        • Language Korean 
        • Length 60 min
        • Title  Recursive techniques
        • Abstract The recursive definition of the Möbius function of a poset provides a recursive technique for computing the reduced Euler characteristic of the order complex of a poset. More refined recursive techniques for computing the homology of a poset are discussed. A general class of posets to which these techniques can be applied, the Cohen-Macaulay posets or more generally the sequentially Cohen-Macaulay posets, are discussed. A recursive formulation of CL-shellability and the recursive techniques for computing Betti numbers are also presented.
        • Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414967012].wmv
        • Reference Poset Topology: Tools and Applications, written by Michelle L. Wachs

      • Lecture BP-1
        • Speaker Boram Park (NIMS)
        • Language Korean 
        • Length 90 min
        • Title List coloring of a graph
        • Abstract A proper coloring of a graph G is a function ϕ defined on V(G) such that ϕ(v)≠ϕ(w) for any two adjacent vertices v and w. The chromatic number of a graph is the smallest integer k such G admits a proper coloring ϕ such that the number of used colors |ϕ(V(G))| is k. A list assignment L of a graph G is a function defined on V(G) such that for each vertex v, L(v) is a finite set. For a positive integer k, for a graph G, we say G is k-choosable if for any list assignment L of G such that |L(v)|=k for any vertex v, there is a proper coloring ϕ of G such that ϕ(v)∈L(v) for any vertex v. The list chromatic number of a graph is the smallest integer k such that G is k-choosable. We will see some results and properties of list coloring of a graph. The List Coloring Conjecture sates that the chromatic number and the list chromatic number of any line graph are the same, and we discuss their related topics as well. In addition, we discuss paintability of a graph as a generalization of the list coloring.
        • Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414766152].wmv
        • Slide Preliminaries: Coloring and List Coloring of Graphs

      • Lecture BP-2
        • Speaker Boram Park (NIMS)
        • Language Korean 
        • Length 90 min
        • Title Alon-Tarsi Theorem
        • Abstract In 1992, N. Alon and M. Tarsi showed that counting even circuits and odd circuits of certain orientation of a graph is related to the list chromatic number of the graph. The circuit C of a digraph is a subset of the arc set such that for any vertex v, the indegree and the outdegree of v in the subdigraph induced by C are the same. A circuit C is even if |C| is even, and C is odd if |C| id odd. Alon-Tarsi Theorem states that if the number of even circuits and the number of odd circuits of an orientation D of a graph G are not the same, then the list chromatic number of G is at most (maximum out-degree of D)+1. In this class, we see the proof of Alon-Tarsi Theorem concisely, then see some results obtained by using Alon-Tarsi Theorem. Brook’s Theorem is one famous theorem in graph coloring, stating that the chromatic number of a graph is bounded by the maximum degree of a graph if the graph is neither a complete graph nor an odd cycle. The list version of Brook’s Theorem is also true, and we could prove it by using Alon-Tarsi Theorem. In addition, if a graph G is a complete graph with odd vertices or a complete bipartite graph, we can obtain the list chromatic number of the line graph of G by using Alon-Tarsi Theorem.
        • Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414100172].wmv
          Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414163222].wmv
        • Slide Graph Coloring and Orientations

      • Lecture SS-1
        • Speaker Seunghyun Seo (Kangwon National University)
        • Language Korean 
        • Length 60 min
        • Title Enumeration of various families of labeled trees: Part I
        • Abstract A labeled tree of size n is a rooted tree consisting of n nodes that are labeled by the set {1,...,n} usually. On labeled trees, we can assign various conditions, which are kinds of restrictions or generalizations. In the 1st talk, we introduce classic families of labeled trees and present the result of their enumeration.
        • Video http://open.nims.re.kr/new/board/upload/event/vod/[20140411854332].wmv

      • Lecture SS-2
        • Speaker Seunghyun Seo (Kangwon National University)
        • Language Korean 
        • Length 60 min
        • Title Enumeration of various families of labeled trees: Part II
        • Abstract A labeled tree of size n is a rooted tree consisting of n nodes that are labeled by the set {1,...,n} usually. On labeled trees, we can assign various conditions, which are kinds of restrictions or generalizations. In the 2nd talk, we discuss the connections to other combinatorial objects such as permutations, partitions, hyperplane arrangements, parking functions, etc.
        • Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414317862].wmv

      • Lecture SS-3
        • Speaker Seunghyun Seo (Kangwon National University)
        • Language Korean 
        • Length 60 min
        • Title Enumeration of various families of labeled trees: Part III
        • Abstract A labeled tree of size n is a rooted tree consisting of n nodes that are labeled by the set {1,...,n} usually. On labeled trees, we can assign various conditions, which are kinds of restrictions or generalizations. In the 3rd talk, we present some recent work on the enumeration of certain labeled trees.
        • Video http://open.nims.re.kr/new/board/upload/event/vod/[20140414898372].wmv

      Registration

      • There is NO registration fee. Just write a registration form until March 21.
      • Due to the budget for 50 persons, we set a limit on the number of participants.
      • In principle, registration is on a first-come, first-served basis. But some special participants could be registered in advance by organizers.
      • So your registration could be refused if the number of registrations is over 50, although you submit your registration form before March 21.

      Accommodation

      • The main hotel of school is Hotel Interciti, which is located at 92, Oncheon-Ro, Yuseong-gu, Daejeon, Korea.
      • The reservations for hotel was already made by NIMS. Please give your name at check-in front after first dinner.
      • Check your roommates in a below list.

      Participants

      Showing 58 items
      English NameOriginal NameAffiliationAccommodationRef.
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      English NameOriginal NameAffiliationAccommodationRef.
      Seunghyun Seo 서승현 Kangwon National Univeristy Room #1013 Organizer & Lecturer 
      Heesung Shin 신희성 Inha University Room #1014 Organizer 
      Sangwook Kim 김상욱 Chonnam National University Room #1012 Lecturer 
      Jang Soo Kim 김장수 Sungkyunkwan University Room #1011 Lecturer 
      Boram Park 박보람 NIMS  Lecturer 
      DoYong Kwon 권도용 Chonnam National University   
      Kyoung-Tark Kim 김경탁 Pusan National University Room #613  
      Minki Kim 김민기 KAIST   
      Sangjib Kim 김상집 Ewha Womans University Room #916  
      Seog-Jin Kim 김석진 Konkuk University   
      Seonhwa Kim 김선화 IBS-CGP Room #915 (April 4)  
      Sooyeong Kim 김수영 Sungkyunkwan University Room #615  
      Younjin Kim 김연진 KAIST   
      Ilhyung Kim 김일형 Seoul National University Room #916  
      Jinha Kim 김진하 Seoul National University Room #612  
      Sunyoung Nam 남선영 Sogang University Room #612  
      Hojoon Ryou 류호준 Gyeonggi Science High School Room #616  
      Sook Min 민숙 Yonsei University Room #912  
      Kyoungsuk Park 박경숙 Ajou University Room #612  
      Kwangsoo Park 박광수 Sungkyunkwan University Room #616  
      Sanggun Park 박상건 Ajou University Room #618  
      YoungJa Park 박영자 Yonsei University Room #911  
      Jihye Park 박지혜 Yeungnam University Room #612  
      Geewon Suh 서기원 KAIST   
      Jeong-woo Seo 서정우 Yeungnam University Room #618  
      Jaebum Sohn 손재범 Yonsei University Room #917  
      Minho Song 송민호 Sungkyunkwan University Room #615  
      Suhyung An 안수형 Yonsei University Room #911  
      Semin Oh 오세민 Pusan National University Room #613  
      Jung Seok Oh 오중석 Seoul National University Room #614  
      Hyonju Yu 유현주 Pusan National University Room #913  
      Heekyung Yu 유희경 Jecheon Girl Middle School Room #913 (April 5)  
      Pilyoung Yoon 윤필영 Seoul National University Room #616  
      Kang-Ju Lee 이강주 Seoul National University Room #614  
      Sang June Lee 이상준 Duksung Women's University Room #915 (April 4)  
      Sang-Jin Lee 이상진 Konkuk University Room #917  
      Seungjang Lee 이승장 JEI University Room #617  
      Seunghun Lee 이승훈 KAIST   
      Euntaek Lee 이은택 Pusan National University Room #617  
      Hyunseok Lee 이현석 Yonsei University Room #617  
      Hui Young Lee 이희영 Hannam University   
      SungBae Lim  임성배 Gyeonggi Science High School Room #616  
      Minjoo Jang 장민주 Yonsei University Room #611  
      Jisu Jeong 정지수 KAIST   
      Ji-Hwan Jung 정지환 Sungkyunkwan University Room #615  
      hyeonyi Jung 정현이 Ewha Womans University Room #611  
      Soojin Cho 조수진 Ajou University   
      Hyung-rok Jo 조형록 Pusan National University Room #613  
      Hyeong-Kwan Ju 주형관 Chonnam National University Room #914  
      Sung-Tae Jin 진성태 Sungkyunkwan University Room #615  
      Seungil Choi 최승일 Sogang University Room #618  
      Jeong Ok Choi 최정옥 GIST Room #912  
      Jungwon Choi 최정원 Gyeonggi Science High School Room #611  
      Jihoon Choi 최지훈 Seoul National University Room #614  
      Hyun il Choi 최현일 Pusan National University Room #613  
      Seungwoo Ha 하승우 Seoul National University Room #614  
      Seoungji Hong 홍성지 Yonsei University Room #914  
      Seoyeon Hwang 황서연 Ewha Womans University Room #611  
      Showing 58 items