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제목 | One-Day Meeting in Combinatorics | |||||||||||||||||||||||||||||||
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작성자 | 관리자 | 등록일 | 2017-09-08 | 조회수 | 257 | |||||||||||||||||||||||||||

One-Day Meeting in Combinatorics
The purpose of the meeting is to collaborate research and foster interaction between
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.
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. |

이전글 | 한국연구재단, AORC 현장평가 컨설팅 |
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다음글 | KIAS-AORC Joint Workshop |