http://matrix.skku.ac.kr/conference/2009-KMS-AMS-CMTSession/ps.html

First Joint International Meeting of the AMS and the Korean Mathematical Society
Seoul, South Korea, December 16-20, 2009 (Wednesday - Sunday)

Schedule of Special Session on Combinatorial Matrix Theory (Code: SS-8A)

• Friday, December 18, 2009, 8:30 a.m - 10:50 a.m.
  
  Room [B501], Ehwa Womans University

Organizers of this session:
Suk-Geun Hwang, Kyungpook National University sghwang@knu.ac.kr with Sang-Gu Lee
Bryan Shader, University of Wyoming, bshader@uwyo.edu with In-Jae Kim

• Chair: Suk-Geun Hwang, Kyungpook National University sghwang@knu.ac.kr

• 8:30 a.m.
  Totally Nonnegative ( 0,1)-Matrices
  Richard A. Brualdi*, WISC, brualdi@math.wisc.edu
  Steve Kirkland, Hamilton Institute, Ireland and University of Regina
  
  Abstract: TBA (KMS submission)
  
  Abstract Number : SS-A8-1019191044
   
• 9:00 a.m.
  The Rules of Divisiblity for Matrices
  Ivo Herzog*, OSU, herzog.23@osu.edu
  
  
  Abstract: TBA (KMS submission)
  
  Abstract Number : SS-A8-1019191147
   
• 9:30 a.m.
  Characterizations of term-rank preservers
  Seok-Zun Song*, Jeju National University, szsong@jejunu.ac.kr
  Kyung-Tae Kang, Jeju National University
  
  Abstract: TBA (KMS submission)
  
  Abstract Number : SS-A8-1019191254
   
• 10:00 a.m.
  Infinite Families of Recursive Formulas Generating Power Moments of Ternary Kloosterman Sums with Square Arguments Associated with O^-(2n,q)
  Dae San Kim*, Sogang University, dskim@sogang.ac.kr
  
  
  Abstract: In this paper, we construct eight infinite families of ternary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the special orthogonal group $SO^{-}(2n,q)$. Here ${q}$ is a power of three. Then we obtain four infinite families of recursive formulas for power moments of Kloosterman sums with square arguments and four infinite families of recursive formulas for even power moments of those in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of $\lq\lq$Gauss sums" for the orthogonal groups $O^{-}(2n,q)$.
  
  Abstract Number : SS-A8-918141716
   
• 10:30 a.m.
  Simultaneous Lyapunov-Sylvester equations for matrices
  Quoc-Phong Vu*, Ohio University, vu@ohio.edu
  Sang-Gu Lee, Sungkyunkwan University
  
  Abstract: We investigate simultaneous solutions of the matrix equations $A_iX-XB_i=C_i, i=1,2,...,k$, where $\{A_i\}$ and $\{B_i\}, i=1,2,...k,$ are commuting k-tuples. We prove that if the joints spectra of the k-tuples $\{A_i\}$ and $\{B_i\} are disjoint, then the equations have a unique common matrix solution for every k-tupple $\{C_i\}, i=1,...,k$ (under some natural compatibility condition on $C_i$) and, conversely, if for every such k-tuple ${C_i}, i=1,...,k$, the equations have a unique common solution, then the joint spectra of the k-tuples $\{A_i\}$ and $\{B_i\} are disjoint. The results are natural extensions of the classical result on single matrix Lyapunov-Sylvester equation.
  
  Abstract Number : SS-A8-930164946
  

• Saturday, December 19, 2009, 8:30 a.m - 10:50 a.m.
  Special Session on Combinatorial Matrix Theory (Code: SS-8A)
  Room [TBA], Ehwa Women University
  
  Chair: Bryan Shader, University of Wyoming, bshader@uwyo.edu

• 8:30 a.m.
  On graphs with smallest eigenvalue -3
  Jack Koolen*, POSTECH, koolen@postech.ac.kr
  Hye Jin Jang
  
  Abstract: In 1976 Cameron et all showed that essentially all graphs with smallest eigenvalue at least -2 are generalized line graphs. In this talk I discuss graphs with smallest eigenvalue at least -3. In particular, I will show that these graphs behave quite a bit different then those with smallest eigenvalue at least -2.
  
  Abstract Number : SS-A8-1013114322
  
  
• 9:00 a.m.
  Eigenvalues and connectivity of regular graphs
  Sebastian M. Cioaba*, University of Delaware, USA, cioaba@math.udel.edu
  
  
  Abstract: In this talk, I will discuss some old and new results relating the connectivity of a regular graph to its eigenvalues.
  
  Abstract Number : SS-A8-924004258
   
• 9:30 a.m.
  On the largest eigenvalues of bipartite graphs which are nearly complete
  In-Jae Kim*, Minnesota State University, Mankato, in-jae.kim@mnsu.edu
  Yi-Fan Chen, Hung-Lin Fu, National Chiao Tung University, Eryn Stehr, Minnesota State University, Mankato, Bredon Watts, University of Oklahoma, Norman
  
  Abstract: The topological structure of a graph, consisting of vertices and edges, can be described in an algebraic object such as the $(0,1)$ adjacency matrix of the graph. It is well known that spectral properties of the adjacency matrix of a graph are closely related to its graph theoretic properties. We even say that the eigenvalues of the adjacency matrix of the graph are the eigenvalues of the graph. In this talk some results on the largest eigenvalues of bipartite graphs are presented. We first compute the largest eigenvalues of a specific class of bipartite graphs which are nearly complete, and then list nearly complete bipartite graphs according to the magnitudes of their largest eigenvalues. These results are related to a conjecture in [A. Bhattacharya, S. Friedland and U.N. Peled, On the first eigenvalue of bipartite graphs, \emph{Electronic Journal of Combinatorics} 15 (2008) $\#$R144].
  
  Abstract Number : SS-A8-921221534
   
• 10:00 a.m.
  On conjectures involving Laplacian eigenvalues and signless Laplacian eigenvalues of graphs
  Kinkar Ch. Das*, Sungkyunkwan University, kinkar@mailcity.com
  
  
  Abstract: Let G=(V,E) be a simple graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the Laplacian matrix of G is L(G)=D(G)-A(G) and the signless Laplacian matrix of G is Q(G)=D(G)+A(G). Cvetkovic et al. (D. Cvetkovic, P. Rowlinson, S. K. Simic, Eigenvalue bounds for the signless Laplacian, Publ. Inst. Math. (Beogr.) (N.S.) 81 (95) (2007) 11-27.) have given a series of 30 conjectures on Laplacian eigenvalues and signless Laplacian eigenvalues of G (see also, M. Aouchiche, P. Hansen, A survey of automated conjectures in spectral graph theory, Linear Algebra Appl., in press). In this paper we prove some of them.
  
  Abstract Number : SS-A8-929202047
   
• 10:30 a.m.
  A generalization of Temperley's tree-number formula and applications in networks
  Woong Kook *, University of Rhode Island, andrewk@math.uri.edu
  Seung Kyoon Shin, University of Rhode Island
  
  Abstract: In 1964, Temperley proved a formula for the tree-number $k(G)$ of a finite graph $G$ with $n$ vertices: $n^{2}k(G)=\det(L(G)+J)$, where $L(G)$ is the Laplacian matrix of $G$ and $J$ is the matrix each of whose entries is +1. In this paper we will prove a generalization of this formula: $um=\det(M+U)$, where $M$ is a matrix such that the sum of the entries in each row and each column is zero, $U$ a rank 1 matrix, $m$ the value of any cofactor of $M$, and $u$ the sum of all entries in $U$. As an application of this generalization, we give a simple and elegant combinatorial interpretation of the amount of information contained in all possible paths between a pair of nodes in a weighted network $G$ which Stephenson and Zelen calculated in 1989 by inverting the matrix $L(G)+J$.
  
  Abstract Number : SS-A8-929080419

 

• Saturday, December 19, 2009, 2:30 p.m - 5:50 p.m.
  Special Session on Combinatorial Matrix Theory (Code: SS-8A)
  Room [TBA], Ehwa Women University
  Organizers of this session:
  Suk-Geun Hwang, Kyungpook National University sghwang@knu.ac.kr
  Bryan Shader, University of Wyoming, bshader@uwyo.edu
  Chair:
  Richard A. Brualdi, University of Wisconsin, brualdi@math.wisc.edu

• 2:30 p.m.
  Minum rank and skew-symmetric matrices described by a graph
  Bryan Shader*, University of Wyoming, bshader@uwyo.edu
  
  Abstract: TBA (KMS submission)
  
  Abstract Number : NONE
   
• 3:00 p.m.
  A structure of Riordan matrices
  Gi-Sang Cheon*, Sungkyunkwan University, gscheon@skku.edu
  Sung-Tae Jin, Sungkyunkwan University
  
  Abstract: We consider an infinite lower triangular matrix $L=[\ell_{n,k}]_{n,k\in\mathrm{\mathbf{N_{0}}}}$ and a sequence $\Omega=(\o_n)_{n\in\mathrm{\mathbf{N_{0}}}}$ such that every element $\ell_{n+1,k+1}$ except column 0 can be expressed as a linear combination with coefficients in $\Omega$ of the elements lying on the slanting line $ax-by=0$ starting from $\ell_{n,k}$ i.e., $$ \ell_{n+1,k+1}=\o_{0}\ell_{n,k}+\o_{1}\ell_{n-a,k+b}+\o_{2}\ell_{n-2a,k+2b}+\cdots$$ where $a$ and $b$ are integers with $a+b>0$ and $b\ge0$. This concept generalizes the $A$-sequence of Riordan matrices. As a result, we explore new sequences of a Riordan matrix.
  
  Abstract Number : SS-A8-930092140
   
• 3:30 p.m.
  Hadamard Equivalence on Binary Matrices - New Combinatoral Problem
  Hong-Yeop Song*, Yonsei University, hysong@yonsei.ac.kr
  Ki-Hyeon Park, Yonsei University,
  
  Abstract: TBA (KMS submission)
  
  Abstract Number : SS-A8-1019191214
   
• 4:00 p.m.
  Perfect Matchings in Claw-free Cubic Graphs
  Sang-il Oum*, KAIST, sangil@kaist.edu
  
  Abstract: TBA (KMS submission)
  
  Abstract Number : SS-A8-1019191016
   
• 4:30 p.m.
  The hitting time subgroup, {\L }ukasiewicz paths and Faber polynomials
  Hana Kim*, Sungkyunkwan University, hakkai14@skku.edu
  Gi-Sang Cheon, Sungkyunkwan University, Louis W. Shapiro, Howard University
  
  Abstract: A \L ukasiewicz path (or more briefly L-path) of length $n$ is a lattice path starting at the origin and ending at $(n,0)$ whose steps are of the type $(1,j)$, $j=1,0,-1,-2,\ldots$ and these paths cannot go below the $x$-axis. It is known that the number of all {\L }ukasiewicz paths of length $n$ is the $n$-th Catalan number. The concept of L-paths connects several disparate subjects, the hitting time subgroup of the Riordan group, restricted and unrestricted lattice paths, and the Faber polynomials from complex variables. These connections are the main topic of this talk.
  
  Abstract Number : SS-A8-930103140
   
• 4:55 p.m.
  Comparing Zagreb indices for connected graphs
  Batmend Horoldagva*, Sungkyunkwan University, b_khorlo@yahoo.com
  Sang-Gu Lee, Sungkyunkwan University
  
  Abstract: TBA (KMS submission)
  
  Abstract Number : SS-A8-1019191349
   
• 5:20 p.m.
  Fibonacci sequences and the winning conditions for the blackout game
  Sang-Gu Lee*, Sungkyunkwan University, sglee at skku.edu
  Duk-Sun Kim, Sungkyunkwan University, Faqir M. Bhatti, Lahore Univ of Management Sciences
  
  Abstract: The blackout game(Lightout Game, Merlin Game, $\sigma$+Game) is a popular game on a squareboard. When we toggle a button with black or white color, it changes the color of itself and other buttons which have common edges. It is similar to the ``Reversi(Othello) Game". With this rule, we can win the game when we have a squareboard with all same colors after some clicks. Here we show that the winning conditions for the general $m \times n$ blackout games are related with the determinant of a block triangular matrix generated by a given blackout game. The Fibonacci sequences are used to get the determinant of the block triangular matrix. We investigate some properties of a generalized Fibonacci sequences with a winnable condition for the blackout game. Also, we introduce a JAVA simulation tool that gives us winnable conditions for an arbitrary given $m \times n$ blackout game.
  
  Abstract Number : SS-A8-831100743

IS. Mathematics for Information Sciences, December 18 (Fri.) Room : B137

17:00 – 17:40 Chair: Gi-Sang Cheon(Sungkyunkwan University)

17:00 An analysis of the singular values from the sound information with its preserver and patternization

Duk-Sun Kim*, Sungkyunkwan University,

Sang-Gu Lee, Sungkyunkwan University [IS-3]

ME. Mathematics Education,  December 18 (Fri.) Room : B151

17:00 – 17:20 Chair: Hyung-Bin Park(Mokpo National University)

17:00 Applications of newly developed excel graphers in mathematics education and mathmatical modeling

Kyung-Won Kim*, Sungkyunkwan University,

Sang-Gu Lee, Sungkyunkwan University [ME-2]

P I. Poster Session, December 16 (Wed.) Room : Lobby between B140 and B141

13:00 – 14:20

13:00 Mathematicians card and poster

Sang-Gu Lee, Sungkyunkwan University,

Duk-Sun Kim, Sungkyunkwan University,

Kyung-Won Kim*, Sungkyunkwan University,

Rae-Young Ko, Sungkyunkwan University [P I-1]

Prof. Richard Brualdi SKKU Talk (2009-12-15, Movie by SGLee)

Prof. Bryan Shader SKKU Talk (2009-12-15, Movie by SGLee)

* Fairwell Gathering

KMS (Korean Mathematical Society)
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