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제목 One-Day Meeting in Combinatorics
작성자 관리자 등록일 2017-09-08 조회수 99

One-Day Meeting in Combinatorics


Applied Algebra and Optimization Research Center(AORC)
Sungkyunkwan University, Korea
September 13 (Wednesday), 2017, AORC Seminar Room

 Schedule 

Time Speaker Title
9:30 - 10:00 Coffee  
10:00 - 11:00 Jeff Remmel (UCSD) Stieltjes moment sequences of polynomials
11:00 - 12:00 Sergey Kitaev (U. Strathclyde) An introduction to the theory of word-representable graphs
12:00 - 14:00 Lunch  
14:00 - 15:00 Ji-Hwan Jung (SKKU-AORC) On Riordan Graphs
15:00 - 16:00 Jihoon Choi (SNU-AORC) Competition graphs of d-partial orders
16:00 - 17:00 Jang Soo KIM (SKKU-AORC) Combinatorics of the Selberg integral
17:30 - Dinner  

 

Purpose

 The purpose of the meeting is to collaborate research and foster interaction between
researchers interested in combinatorics and related topics. Hopefully, the meeting will
provide a convenient platform for the exchange of research experiences and ideas
from different research areas related to combinatorics. Anyone interested is welcome
to attend. For any inquiries, please contact Jang Soo Kim (jangsookim@skku.edu).

 

Abstract

Speaker: Jeff Remmel (UCSD, USA)
Title: Stieltjes moment sequences of polynomials

A sequence is Stieltjes moment sequence if it has the form for is a non-negative
measure on. It is known that is Stieltjes moment sequence if and only if the matrix
is totally positive, i.e., all its minors are non-negative. We define a sequence of
polynomials in to be Stieltjes moment sequence of polynomials if the matrix is totally
positive, i.e., all its minors are polynomials in with non-negative coefficients. We
shall show that one can construct a large number of examples Stieltjes moment
sequence of polynomials by finding multivariable analogues of Catalan-like numbers
as defined by Aigner.
This is joint work with Huyile Liang and Sai-nan Zheng of Dalian University of
Technology.

Speaker: Sergey Kitaev (University of Strathclyde, UK)
Title: An introduction to the theory of word-representable graphs

Letters x and y alternate in a word w if after deleting in w all letters but the copies of
x and y we either obtain a word xyxy… (of even or odd length) or a word yxyx… (of
even or odd length). A graph G=(V,E) is word-representable if and only if there
exists a word w over the alphabet V such that letters x and y alternate in w if and
only if xy in E.
Word-representable graphs generalize several important classes of graphs such as
circle graphs, 3-colorable graphs and comparability graphs. In this talk, I will give a
comprehensive introduction to the theory of word-representable graphs. In particular,
I will discuss the characterization of word-representable graphs in terms of
semi-transitive orientations.

Speaker: Ji-Hwan Jung (SKKU, Korea)
Title: On Riordan Graphs

In this talk, we use the theory of Riordan matrices to introduce the notion of a Riordan
graph. The Riordan graphs are a far-reaching generalization of the well known and
well studied Pascal graphs and Toeplitz graphs, and also some other families of
graphs. The Riordan graphs are proved to have a number of interesting (fractal)
properties, which can be useful in creating computer networks with certain desired
features, or in obtaining useful information when designing algorithms to compute
values of graph invariant. The main focus in this paper is the study of structural
properties of families of Riordan graphs obtained from infinite Riordan graphs, which
includes a fundamental decomposition theorem and the generalization of some known
results for the Pascal graphs.

Speaker: Jihoon Choi (SNU, Korea)
Title: Competition graphs of d-partial orders

The competition graph C(D) of a digraph D is defined to be an undirected graph which
has the same vertex set as D and which has an edge joining two distinct vertices x and
y if and only if there are arcs (x,z) and (y,z) for some vertex z in D. Competition
graphs have been extensively studied for more than four decades. Recently, Choi et al.
(2016) introduced a notion of d-partial orders and studied the competition graphs of
d-partial orders. They showed that every graph G is the competition graph of a
d-partial order for some nonnegative integer d and called the smallest such d the
partial order competition dimension, denoted by , of G. This notion extends the
statements that the competition graph of a doubly partial order is interval and that any
interval graph can be the competition graph of a doubly partial order as long as
sufficiently many isolated vertices are added, which were proven by Cho and Kim
(2005). As a matter of fact, these statements can be restated as the statement that
interval graphs are exactly the graphs with .
In this talk, we give a necessary and sufficient condition for a graph G satisfying for
a given positive integer d. Then we present interesting families of graphs G with and
some graphs G with . In addition, we present interesting open problems related to the
partial order competition dimension of graphs.

Speaker: Jang Soo Kim (SKKU, Korea)
Title: Combinatorics of the Selberg integral

Stanley found a combinatorial interpretation of the Selberg integral in terms of
permutations. In this talk we introduce Selberg tableaux which are essentially the
same as those permutations. We will present a simple relation between the number of
Selberg tableaux and the number of Young tableaux of a shifted staircase shape.

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