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The 5th Combinatorics Seminar in fiscal 2012

Hold Date 2013-01-26 09:30~2013-01-26 17:45

Place Seminar Room I (2F) in Reference Eki Higashi Building. 1-16-14 Hakata-Eki-Higashi, Hakata-Ku, Fukuoka City, 812-0013

Object person  

Speaker Akihiro Munemasa (Tohoku University), Minwon Na (Tohoku University), Michael Dobbins (KAIST), Aleksandar Jurišić (University of Ljubljana), Xiao-Dong Zhang (Shanghai Jiao Tong University), Katsuhiro Ota (Keio University), Yota Otachi (JAIST)

The 5th Combinatorics Seminar in fiscal 2012
Hakata Worksho 2013 on "Combinatorics and its Application"

This is a satellite seminar of the 11th Japan-Korea Workshop on Algebra and Combinatorics. Our purpose of this meeting is giving an opportunity to make a speech and to commuticate with reserchers who study verious fields not only Combinatorics.

Further information is available from the organizers below.



9:30--10:05 Akihiro Munemasa (Tohoku University)
Title:Complex Hadamard matrices contained in a Bose-Mesner algebra
A complex Hadamard matrix is an n by n matrix with complex H entries with absolute value 1, such that rows are pairwise orthogonal with respect to the hermitian inner product. Recently, Ada Chan constructed a 15 by 15 complex Hadamard matrix using the adjacency matrix of the line graph of the Petersen graph. We found another such matrix, and then generalized it to an infinite family. In this talk, we focus on how to set up a system of polynomial equations for solving this kind of problem more efficiently than the naive approach. This is achieved by determining the ideal of the 3-dimensional algebraic variety consisting of the points of the form (x+1/x,y+1/y,z+1/z,x/y+y/x,y/z+z/y,z/x+x/z) in the 6-dimensional space. This is a joint work with Takuya Ikuta.

10:10--10:45 Minwon Na (Tohoku University)

11:00--11:35 Michael Dobbins (KAIST)

11:40--12:15 Aleksandar Jurišić (University of Ljubljana)

12:20--15:10 Poster Session 「Introduction to Mathematical Software」(in Japanese)

15:15--16:15 Xiao-Dong Zhang (Shanghai Jiao Tong University)
Title:The algebraic connectivity of graphs
Let G be a simple graph of order n and L(G)=D(G)-A(G) be its Laplacian matrix, where D(G) and A(G) are the degree diagonal and adjacency matrices, respectively. The the second smallest eigenvalue of L(G) is called the algebraic connectivity of G. In this talk, we survey some new results and progress on the algebraic connectivity. In particular, we present some relationships between the algebraic connectivity and the graph parameters, such as the clique number, the matching number, the independence number, the isoperimetric number, etc.

16:30--17:05 Katsuhiro Ota (Keio University)
17:10--17:45 Yota Otachi (JAIST)
Title:The path-distance-width of hypercubes
The path-distance-width of a connected graph G is the minimum integer ω satisfying that there is a nonempty subset of SV(G)such that the number of the vertices with distance i from S is at most ω for any nonnegative integer i . We present a general lower bound on the path-distance-width of graph, and determine the path-distance-width of hypercubes by using the lower bound. We also discuss the applicability of the lower bound to other graphs.

This seminar supported by Global COE Program "Education and Research Hub for Mathematics-for-Industry"