### Programs

Plans of the Main Program

Tentative Programs

### First Joint International Meeting of the AMS and the Korean Mathematical SocietySeoul, South Korea, December 16-20, 2009 (Wednesday - Sunday)Meeting #1055

Tentative Program Schedule
(This schedule is tentative so, it should be modified.)

• Friday, December 18, 2009, 8:30 a.m - 10:50 a.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:
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

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

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
Organizers of this session:
Suk-Geun Hwang, Kyungpook National University sghwang@knu.ac.kr
Bryan Shader, University of Wyoming, bshader@uwyo.edu
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

Bryan Shader*, University of Wyoming, bshader@uwyo.edu

Abstract: TBA (KMS submission)

Abstract Number : NONE

• 3:00 p.m.
An algebraic 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

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

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@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

* If we have one more talk, we may add at 5:45 p.m.

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Copyrights © 2009. Sungkyunkwan University, Prof. Sang-Gu Lee. All rights reserved.