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제목 One-Day Meeting in Combinatorics
작성자 관리자 등록일 2017-09-21 조회수 157

 

Jeffrey Remmel (Univ. of California, San Diego, USA) 

Title: Stieltjes moment sequences of polynomials

Date: 10:00 - 11:00, Sep. 13, 2017 (AORC Seminar Room)

  

 

Abstract:

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.

 

 

 

Sergey Kitaev (Univ. of Strathclyde, UK)                     

Title: An introduction to the theory of word-representable graphs

Date: 11:00 - 12:00, Sep. 13, 2017 (AORC Seminar Room)

 

 

Abstract:

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.

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다음글 Special Lecture Series of AORC Working Workshop (May 22 ~ June 2, 2017)
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