- 追加された行はこの色です。
- 削除された行はこの色です。
* 九州大学 代数・組合せ数学 日韓合同ワークショップ [#m322cc3e]
''～ Japan-Korea Workshop on Algebra and Combinatorics ～''
#br
The 11th Japan-Korea Workshop on Algebra and Combinatorics will take
place at Fukuoka City in Japan, from 24-25, January 2013. The workshop
is held once a year, alternatively in Japan and in Korea. It is intended to
provide researchers of both countries, especially young researchers including
graduate students, with opportunities to exchange rather informal information
of ongoing studies in the area.
Further information is available from the organizers below.
[[&ref(./Japan-Korea Workshop on Algebra and Combinatorics.jpg,nolink,40%);>http://comb.math.kyushu-u.ac.jp/?plugin=attach&pcmd=open&file=Japan-Korea%20Workshop%20on%20Algebra%20and%20Combinatorics.pdf&refer=20130124]]
**Organizers [#xb11a6e1]
Eiichi Bannai (Shanghai Jiao Tong University)
Jung Rae Cho (Pusan National University)
Mitsugu Hirasaka (Pusan National University)
Tatsuro Ito (Kanazawa University)
Hyun Kwang Kim (POSTECH)
Jack Koolen (POSTECH)
[[Yoshihiro Mizoguchi:http://imi.kyushu-u.ac.jp/~ym/]] (Kyushu University),~
Akihiro Munemasa (Tohoku University)
-Eiichi Bannai (Shanghai Jiao Tong University)
-Jung Rae Cho (Pusan National University)
-Mitsugu Hirasaka (Pusan National University)
-Tatsuro Ito (Kanazawa University)
-Hyun Kwang Kim (POSTECH)
-Jack Koolen (POSTECH)
-[[Yoshihiro Mizoguchi:http://imi.kyushu-u.ac.jp/~ym/]] (Kyushu University),~
-Akihiro Munemasa (Tohoku University)
**Supported by [#l7bc435b]
-[[グローバルCOEプログラム「マス・フォア・インダストリ研究教育拠点」:http://gcoe-mi.jp/]]
[[Global COE Program "Education and Research Hub for Mathematics-for-Industry":http://gcoe-mi.jp/]]
-[[科学研究費補助金基盤(S) 課題番号20224001 研究代表者 中尾 充宏:http://kaken.nii.ac.jp/d/p/20224001]]
[[Grant-in-Aid for Scientific Research (S) (Research Project Number: 20224001, Principal Investigator: Mitsuhiro Nakao):http://kaken.nii.ac.jp/en/p/20224001]]
**Date [#cdeebbd2]
-January 24, 2013. 10:00-18:00
-January 25, 2013. 10:00-18:00
**Location [#ec2c564b]
-Seminar Room 2 in ACROS Fukuoka Foundation
1-1-1 Tenjin, Chuo-ku, Fukuoka City, 810-0001
(see http://www.acros.or.jp/english/access/)
(see http://www.acros.or.jp/english/access/ )
**Accommodation [#l5050a6e]
The place of the workshop is located at Tenjin area which is in the center of
Fukuoka City and closed to Nakasu and Hakata. You can find many hotels
around Tenjin, Nakasu or Hakata (see http://www.booking.com/ ).
**Satellite Seminar [#b9ed65a1]
In 26th of January a workshop entitled as
Hakata Workshop 2012 on "Combinatorics and its Applications"
will be held at Reference Rental Meeting Room
(see http://www.re-rental.com/index.html) in Hakata area.
**Program [#a25b6bb0]
***January 24 (Thursday) at Room 2 in ACROS Fukuoka [#a4c7bcdc]
-Openning Speech Yoshihiro Mizoguchi
-Chair: Akihiro Munemasa
-10:00-10:45 Ferenc Szollosi(Tohoku University)
-10:00-10:45 Ferenc Szöllősi(Tohoku University)
--Modular combinatorial designs and Hadamard matrices modulo 5
-11:00-11:45 Gary Greaves (Tohoku University)
--TBA
-Chair: Mitsugu Hirasaka
-13:30-14:15 Shun'ichi Yokoyama (Kyushu University / JST CREST)
--Developments in Computer Algebra Research: the Next Generation
-14:30-15:45 Takao Komatsu (Hirosaki University)
--Minimal polynomials of integer symmetric matrices
-Chair: Jung Rae Cho
-13:30-14:15 Ryuzaburo Noda
--Some bounds for the number of Blocks
-14:30-15:15 Takao Komatsu (Hirosaki University)
--Poly-Cauchy numbers and their combinatorial properties
-Chair: Hyun Kwang Kim (POSTECH)
-16:00-16:45 Jong Yoon Hyun (Ewha Womans University)
--A new family of strongly regular graphs using weakly regular p-ary bent functions
-17:00-17:45 Phan Thanh Toan (POSTECH)
--TBA
-15:45-16:30 Jong Yoon Hyun (Ewha Womans University)
--A new family of strongly regular graphs using weakly regular '''p'''-ary bent functions
-16:45-17:30 Phan Thanh Toan (POSTECH)
Counting methods and upper bounds on sizes of codes
***January 25 (Friday) at at Room 2 in ACROS Fukuoka [#b08196cb]
-Chair: Eiichi Bannai
-10:00-10:45 Xiao-Dong Zhang (Shanghai Jiao Tong University)
--The Dirichlet eigenvalues of graphs and the Faber-Krahn Inequality
-11:00-11:45 Ryuzaburo Noda
--Some upper bound for the number of blocks in block designs
-11:00-11:45 Shun'ichi Yokoyama (Kyushu University / JST CREST)
--Developments in Computer Algebra Research: the Next Generation
-Chair: Tatsuro Ito
-13:30-14:15 Joon Yop Lee (POSTECH)
--Multidimensional matrices uniquely recovered by their lines
-14:30-15:45 Satoshi Tsujimoto (Kyoto University)
-14:30-15:15 Satoshi Tsujimoto (Kyoto University)
--Dunkl shift operators and Bannai-Ito polynomials
-Chair: Jack Koolen
-16:00-16:45 Andreas Holmsen (KAIST)
--TBA
-17:00-17:45 Jon-Lark Kim (Sogang University)
--TBA
-Closing Speech Yoshihiro Mizoguchi
-15:45-16:30 Andreas Holmsen (KAIST)
--Generalized wiring diagrams, realization spaces, and configurations of convex sets
-16:45-17:30 Jon-Lark Kim (Sogang University)
--A new class of error-correcting codes for Boolean masking of cryptographic computations
-Closing Speech Mitsugu Hirasaka
**Abstract [#c2089740]
***吴耀琨（上海交通大学） [#wu-05]
Yaokun Wu (Shanhai Jiao Tong University)
-Title: Some combinatorial analysis of infinite matrix product
***Gary Greaves (Tohoku University) [#wu-05]
-Title: Minimal polynomials of integer symmetric matrices
-Abstract:
The minimal polynomial of an integer symmetric matrix must be
monic and must have integer coefficients and distinct real zeros. In this talk
we will discuss advances about the extent to which these necessary condi-
tions are sufficient and we will present some recent classifications of integer
symmetric matrices having their spectral spread less than 4.
***Jong Yoon Hyun (Ewha Womans University) [#ozeki-05]
-Title: A new family of strongly regular graphs using weakly regular '''p'''-ary bent functions
-Abstract:
The infinite product of a nonnegative square matrix is well
understood thanks to the Perron-Frobenius Theory. In many contexts, say
inhomogeneous Markov chain or opinion dynamics,
one needs to consider the infinite product of several nonnegative
square matrices of the same size. This general problem is much more
complicated and seems that there is not any systematic
theory for the analysis of the relevant dynamical behavior yet.
We construct strongly regular graphs and association schemes by
using the weakly regular '''p'''-ary bent functions (from &mimetex{Z^n_p}; to &mimetex{Z_p};), where '''p''' is a prime number. We obtain some useful sign function formulae for those functions, and these formulae are used for development of our main result. In fact, we find a new family of strongly regular graphs.
In this talk, we will discuss some combinatorial results obtained by
the speaker and others (to be named during the lecture) on the dynamical
behavior of the infinite matrix product of
a set of matrices (of some special forms).
***小関 健太（国立情報学研究所） [#ozeki-05]
Kenta Ozeki (National Institute of Informatics, Japan)
-Title: On the Hamiltonicity of graphs on a surface
***Andreas Holmsen (KAIST) [#chen-05]
Xiaojun Chen (The Hong Kong Polytechnic University)
-Title: Generalized wiring diagrams, realization spaces, and configurations of convex sets
-Abstract:
A cycle in a graph '''G''' is called Hamiltonian if it passes through all
vertices in '''G'''. In this talk, we will concentrate on a Hamiltonian cycle
in graphs on a Topological surface, for example, the sphere (the plane),
the projective plane, the torus, and so on. One of the most classical
result of this area is the one due to Tutte that stats that “every
4-connected plane graph has a Hamiltonian cycle”. I would like to
introduce some other results, some of which are obtained very recently. I
also mention the connection between “the toughness” and the
Hamiltonicity of graphs on a surface.
Wiring diagrams were introduced by J.Goodman in 1980 as a com-
binatorial encoding of planar point configurations. Together with M.Dobbins
and A.Hubard, we generalize this and consider the "wiring monoid" gener-
ated by simple the simple transpositions. I will characterize certain highly
regular substructures of the wiring monoid and show how this resolves a con-
jecture of Pach and Toth in geometric Ramsey theory, by using a geometric
representation theorem for generalized wiring diagrams. This also gives rise
to the notion of Realization spaces for which I will describe our Universality
result.
This is a joint work with K. Kawarabayashi (National Institute of
Informatics, Japan).
***Jon-Lark Kim (Sogang University) [#k063c5c8]
Title: A new class of error-correcting codes for Boolean masking of cryptographic computations
Abstract:
We introduce a new class of rate one half binary codes: complementary
information set codes. A binary linear code of length 2n and dimension
n is called a complementary information set code (CIS code for short) if it
has two disjoint information sets. This class of codes contains self-dual codes
as a subclass. It is connected to graph correlation immune Boolean functions
of use in the security of hardware implementations of cryptographic
primitives. Such codes permit to improve the cost of masking cryptographic
algorithms against side channel attacks. In this talk we investigate this new
class of codes: we give optimal or best known CIS codes of length ｡ 132. We
derive general constructions based on cyclic codes, double circulant codes,
and 2-class association schemes. We derive a Varshamov-Gilbert bound for
long CIS codes, and show that they can all be classified in small lengths up to
12 by the building up construction. Some nonlinear S-boxes are constructed
by using Z4-codes, based on the notion of dual distance of an unrestricted
code. This is a joint work with C. Carlet, P. Gaborit, and P. Sole.
***陳小君（香港理工大学） [#chen-05]
Xiaojun Chen (The Hong Kong Polytechnic University)
-Title: Computational Existence Proofs for Spherical '''t'''-Designs
-Abstract:
***Takao Komatsu (Hirosaki University) [#o2e61762]
Title: Poly-Cauchy numbers and their combinatorial properties Abstract:
We introduce some generalized poly-Cauchy numbers and show some com-
binatorial properties. (to be updated)
Spherical '''t'''-designs provide quadrature rules for the sphere which
are exact for polynomials up to degree '''t'''. In this talk, we
propose a computational algorithm based on interval arithmetic
which, for given '''t''', upon successful completion will have proved
the existence of a '''t'''-design with &mimetex{(t+1)^2}; nodes and will have
computed narrow interval enclosures which are known to contain these
nodes with mathematical certainty. Since there is no theoretical
result which proves the existence of a '''t'''-design with &mimetex{(t+1)^2};
nodes for arbitrary '''t''', our method contributes to the theory
because it was tested successfully for '''t'''＝ 1, 2, ..., 100, i.e.,
for all '''t''' considered so far. The '''t'''-design is usually not
unique; our method aims at finding a well-conditioned one. The
method relies on computing an interval enclosure for the zero of a
highly nonlinear system of dimension &mimetex{(t+1)^2};. We therefore develop
several special approaches which allow us to use interval arithmetic
efficiently in this particular situation. The computations were all
done using the MATLAB toolbox INTLAB. At the end of this talk,
applications of well conditioned spherical designs for integration, interpolation and
regularized least squares approximations on the
two-sphere are discussed.
***Joon Yop Lee (POSTECH) [#x73521df]
-Title: Multidimensional matrices uniquely recovered by their lines
-Abstract:
Joint work with Congpei An, Andreas Frommer, Bruno Lang, Ian Sloan and Womersley.
We provide a method to determine if a '''q'''-ary multidimensional
matrix is lonesum or not by using properties of linesums of lonesum mul-
tidimensional matrices. In particular, we establish a graphic method that
uses edge-colored graphs to determine if a binary multidimensional matrix is
lonesum or not. We also provide two methods to determine if a '''q'''-ary mul-
tidimensional matrix is lonestructure or not. The first one uses properties
of line structures of lonestructure multidimensional matrices and the second
one uses edge-colored directed multigraphs.
''References''~
[1] C. An, X. Chen, I. H. Sloan and R. S. Womersley, Well conditioned
spherical designs for integration and interpolation on the
two-sphere, SIAM J. Numerical Analysis, 48(2010), 2135—2157.~
[2] C. An, X. Chen, I. H. Sloan and R. S. Womersley,
Regularized least squares approximations on the sphere using spherical designs,
submitted to SIAM J. Numerical Analysis, under revision.~
[3] X. Chen, A. Frommer and B. Lang, Computational existence proofs for
spherical '''t'''-designs, Numerische Mathematik, 117(2011), 289—305.~
[4] X. Chen and R. S. Womersley, Existence of solutions to systems of
underdetermined equations and spherical designs, SIAM J. Numerical
Analysis, 44(2006), 2326—2341.~
[5] X. Chen, R. S. Womersley and J. J. Ye,
Minimizing the condition number of a Gram matrix, SIAM J. Optimization, 21(2011), 127—148.
***Ryuzaburo Noda [#z9fc8919]
-Title: Some upper bound for the number of blocks in block designs
-Abstract:
Definition. A design '''D''' = (''', B''') is called a design with parameters
set ('''v, k, d''') or simply a ('''v, k, d''') design if |'''Ω'''| = '''v''', block size='''k''' and the
maximal intersection number of two blocks='''d'''.
***木村 拓馬（佐世保工業高等専門学校），木下 武彦（京都大学数理解析研究所），中尾 充宏（佐世保工業高等専門学校） [#kimura-05]
Takuma Kimura (Sasebo National College of Technology),
Takehiko Kinoshita (RIMS, Kyoto University)
and Mitsuhiro T. Nakao (Sasebo National College of Technology)
-Title: A numerical method to prove the existence of solutions for nonlinear parabolic problems
-Abstract:
We do not assume that '''D''' is a '''t'''-design, though it proves to be a certain t-
design if some natural upper bound for the number of blocks of '''D''' is achieved.
The following lemma is simple but fundamental.
We present numerical verification methods for parabolic problems.
Our main result is a constructive a posteriori estimates of inverse
operators for initial-boundary value problems in linear parabolic PDEs
on a bounded domain.
Lemma. Let '''D''' be a ('''v, k, d''') design. Then for any point subset '''X''' of size
'''d + 2i - 1''', where '''i''' is an arbitrary integer, there exists at most one block '''B'''
such that |'''X''' ⋂ '''B'''| is larger than or equal to '''d + i'''.
The proposed a posteriori estimates is based on error analysis of the
Galerkin approximation for boundary value problems in space direction
and the piecewise linear interpolation for initial value problems in time.
Applying the result, we can numerically prove the existence of solutions
for nonlinear parabolic initial-boundary value problems.
Some numerical results will be shown in the talk.
In [2] and [3] ,by making use of the above lemma,the natural upper bound
for the number of blocks in a ('''v, k, d''') design is given and it is proved in the
case '''i = 2''' that the bound is achieved if and only if it is a '''t'''-design for a
certain t which is the zero of some polynomial of t with coefficients from '''v''',
'''k''' and '''d'''. First I will show the results in [2],[3] and then show some recent
developments .The relation with perfect '''e'''-codes in Johnson scheme is also
shown.
[1]P.Hauck, Eine Charakterisierungdes Steiner systems J. Comb. Theory,
Ser.A, 32(1982)
***田中 守（東北大学大学院 理学研究科） [#tanaka-05]
Mamoru Tanaka (Tohoku University)
-Title: Higher eigenvalues of the Laplacian on a graph and partitions of the graph
-Abstract:
[2]R.Noda, Some Bounds for the number of Blocks, Europ. J.
Combinatorics, 22 (2001) 91-94
We can regard the 2-nd eigenvalue of the Laplacian on a
connected finite graph as strength
of connection between two disjoint subgraphs in the graph. In this
talk, I will give a relation
between the '''k'''-th eigenvalue of the Laplacian on a connected finite
graph and the minimum among the
2-nd eigenvalues of the Laplacians on the subgraphs in a partition of the graph.
[3]R.Noda, Some Bounds for the number of Blocks II, Europ. J.
Combinatorics, 22 (2001) 95-100
[4] T.Etzion, Perfect constant-weight codes IEE Transactions on
Information Theory Vol.50, No9, September, 2004
***平坂 貢（釜山国立大学） [#hirasaka-05]
Mitsugu Hirasaka (Pusan National University)
-Title: Characterization of '''p'''-valenced association schemes
***Ferenc Szöllősi(Tohoku University) [#u0c0c864]
-Title: Modular combinatorial designs and Hadamard matrices modulo 5
-Abstract:
Let '''m > 2''' be an integer. An '''m'''-modular Hadamard matrix &mimetex{H}; of
order '''n''' is an '''n × n''' matrix with ('''-1, 1''') entries such that
&mimetex{HH^T \equiv nI};('''mod m''').
In this talk we report on our recent advances regarding the existence of mod-
ular Hadamard matrices. By introducing a new concept, called m-modular
symmetric designs, we were able to give a complete classification of 5-modular
Hadamard matrices. This is a joint work with Prof. Moon Ho Lee.
***Phan Thanh Toan (POSTECH) [#aa646932]
-Title: Counting methods and upper bounds on sizes of codes
-Abstract:
We study error-correcting codes over &mimetex{Z_q};, where '''q ≧ 2''' is an integer.
We prove (and reprove) several upper bounds on sizes of codes by using
counting methods. Explicit new upper bounds are given.
***Satoshi Tsujimoto (Kyoto University) [#wcadc188]
-Title: Dunkl shift operators and Bannai-Ito polynomials
-Abstract:
We consider the operator which contains the first order shift operator and the reflac-
tion operator, that we call Dunkl shift operator. Then the Bannai-Ito poly-
nomials can be introduced as a sequence of the polynomial eigenfunctions of
the Dunkl shift operator. We will discuss various aspects of the Bannai-Ito
polynomials from the viewpoint of classical orthogonal polynomials.
***Shun'ichi Yokoyama (Kyushu University / JST CREST) [#n1c54a33]
-Title: Developments in Computer Algebra Research: the Next Generation
-Abstract:
Producing computer algebra systems and related services (almost
all are non-commercial) has been of great value in mathematical research.
Recently, high-quality several web-based software development environments
are born. They are highly interactive and much more focused on math al-
gorithms, education, and pure mathematics research (e.g. algebra and com-
binatorics) of course. In this talk, we introduce some of CAS-development
projects that are currently going on.
***Xiao-Dong Zhang (Shanghai Jiao Tong University) [#m7eb3533]
-Title: The Dirichlet eigenvalues of graphs and the Faber-Krahn Inequality
-Abstract:
Let &mimetex{(X, \, \{R_i\}_{0 \leq i \leq d})}; be an assocaition scheme
and '''p''' a prime.
We say that &mimetex{(X, \, \{R_i\}_{0\leq i \leq d})}; is '''p'''-valenced if &mimetex{k_i}; is
a power of '''p'''
for each '''i''' with &mimetex{0 \leq i \leq d}; where &mimetex{k_i}; is the constant
out-degree of the digraph &mimetex{(X, \, R_i)};.
In this talk we show some conditions for a '''p'''-valenced association scheme to be
induced by a transitive permutation group.
The Faber-Krahn inequality in the Riemannian manifolds states
that the ball has minimal first Dirichlet eigenvalue among all bounded do-
mains with the fixed volume in &mimetex{R^n};. In this talk, we will introduce the concept
of a "graph with boundary " and formulated the Dirichlet eigenvalue problem
for graphs. Then survey some new results and progress on the Faber-Krahn
inequality of graphs and the first Dirichlet eigenvalues of graphs.
Joint work with Congpei An, Andreas Frommer, Bruno Lang, Ian Sloan and Womersley.
''References''~
