RIMS Symposium on Algebraic Combinatorics 1998

Program

• Monday, December 14, 1998 : 10:00 am - 4:45 pm
• Tuesday, December 15, 1998 : 10:00 am - 5:05 pm
• Wednesday, December 16, 1998 : 10:00 am - 5:00 pm

Monday, December 14, 1998

• 10:00 am - 11:00 am
  Name : Eiichi Bannai, 坂内英一
  Affiliation : Department of Mathematics, Kyushu University
  Title : Open problems of algebraic combinatorics on spheres
  Abstract :
  

• 11:10 am - 12:10 am
  Name : Kenichiro Tanabe, 田辺顕一朗
  Affiliation : Graduate School of Mathematics, Kyushu University
  Title : On designs in codes over Z₄
  Abstract : The Assmus-Mattson theorem is a classical result on designs in linear codes over a finite field. I will talk about an analoguous result of this theorem for Z₄-codes.
  

• Lunch Time

• 1:30 pm - 2:00 pm
  Name : Masaaki Harada, 原田昌晃, (with Eiichi Bannai, Akihiro Munemasa, and Manabu Oura (Kyushu Univ.))
  Affiliation : Department of Mathematics, Yamagata University
  Title : Type II codes over F₂+uF₂ and an application to Hermitian modular forms
  Abstract :
  

• 2:10 pm - 2:35 pm
  Name : Mitsuhiro Sawano, 澤野 光弘
  Affiliation : Graduate School of Mathematics, Kyushu University
  Title : Four-weight spin models with exactly two values and regular Hadamard designs
  Abstract :
  

• 2:40 pm - 3:05 pm
  Name : Takuya Ikuta, 生田卓也, (with Kazumasa Nomura (Tokyo Medical and Dental College))
  Affiliation : Kobe Gakuin Women's College
  Title : General form of non-symmetric spin models
  Abstract : A spin model (for link invariants) is a square matrix W with non-zero complex entries which satisfies certain axioms. Recently in the paper of F.Jaeger and K.Nomura "Symmetric Versus non-symmetric spin models for link invariants", it was shown that ^tW W^-1 is a permutation matrix (the order of this permutation matrix is called the "index" of W), and a general form was given for spin models of index 2. In this lecture, we generalize this general form to an arbitrary index m. In particular, we give a simple form of W when m is a prime number.
  

• 3:20 pm - 3:45 pm
  Name : Norio Yamazaki, 山崎則男
  Affiliation : Department of Mathematics, Kyushu University (JSPS Research Fellow)
  Title : On a combinatorial approach to some Cayley graphs
  Abstract :
  

• 3:50 pm - 4:15 pm
  Name : Masato Tomiyama, 冨山正人
  Affiliation : Department of Mathematics, Ishikawa National College of Technology
  Title : On the group association scheme of W(E₆)
  Abstract : The group association scheme of X(G) can be constructed from each finite group G. For a given group G, it is an interesting problem to characterize X(G) by its intersection numbers. We consider the characterization of X(W(E₆)). Though it is not completed, we will talk about the present situation of it.
  

• 4:20 pm - 4:45 pm
  Name : Satoshi Shinohara, 篠原聡，(with Rhyo Fuji-Hara (Institute of Policy and Planning Sciences, University of Tsukuba))
  Affiliation : Systems, Information and Mathematical Sciences Course Doctoral Program in Policy and Planning Sciences, University of Tsukuba
  Title : Algebraic curves and designs with repeated elements in blocks
  Abstract : We consider types of block designs which have multi-set blocks. Let V be a set of points and B a collection of multi-subset of V with size k. A balanced n-ary design is a pair (V,B) satisfying two conditions; each element occurs at most n-1 times in any block, and each unordered pair of distinct elements occurs l times. Note that in the block {x,x,y}, the pair {x,y} is counted two times in the block. A multi-set design (V,B) has the property that every pair (not necessary to be distinct) occurs l times in the blocks of B. We show here some constructions of these designs by using algebraic curves over finite fields.
  

Tuesday, December 15, 1998

• 10:00 am - 11:00 am
  Name : Paul Terwilliger
  Affiliation : Department of Mathematics, University of Wisconsin
  Title : Introduction to Leonard system
  Abstract :
  

• 11:10 am - 11:40 am
  Name : Yutaka Hiramine, 平峰 豊
  Affiliation : Department of Mathematics, Faculty of Education, Kumomoto University
  Title : On Semiregular relative difference sets in non-abelian groups
  Abatract :In this talk we consider semiregular relative difference sets in non-abelian groups having an abelian subgroup of index 2. As an application we give results on semiregular relative difference sets in dihedral groups, semidiheral groups and generalized quaternion groups.
  

• 11:45 am - 12:10 am
  Name : Chihiro Suetake, 末竹千博
  Affiliation : Amagasaki-Minami High School
  Title : Projective planes and Hadamard designs
  Abstract : There are some relations between projective planes with some perspectivities and Hadamard designs.
  

• Lunch Time

• 1:30 pm - 1:55 pm
  Name : Tsuyoshi Atsumi, 厚見寅司
  Affiliation : Department of Mathematics and Computer Science, Faculty of Science, Kagoshima University
  Title : Another proof of Hiramine's theorem on three-dimensional Schur rings
  Abstract : We give another proof to Hiramine's theorem on three-dimensional Schur rings. Our proof, which improves the theorem slightly, is clear and straightforward. The original proof is complicated and ingenious. 　
  

• 2:00 pm - 2:25 pm
  Name : Ching-Hung Lam
  Affiliation : Institute of Mathematics, University of Tsukuba
  Title : Codes and construction of VOA
  Abstract :
  

• 2:30 pm - 2:55 pm
  Name : Fumihito Oda, 小田 文仁
  Affiliation : Department of Mathematics, Hokkaido University, (JSPS Research Fellow)
  Title : On Burnside functors
  Abstract : Burnside functor for a finite group is the unit element of the representation ring of Mackey algebra. Moreover it is the indecomposable projective module for Mackey algebra. I shall talk on some notes about the Loewy structure of Burnside functor.
  

• 3:10 pm - 3:35 pm
  Name : Nobuo Iiyori, 飯寄信保
  Affiliation : Department of Mathematics, Faculty of Education, Yamaguchi University
  Title : A group of functions over a group and its representations
  Abstract :
  

• 3:40 pm - 4:05 pm
  Name : Seiichi Abe, 阿部晴一
  Affiliation : Department of Mathematical Sciences, Graduate School of Yamaguchi University
  Title : On generalized prime graphs
  Abstract : We will discuss some generalizations of prime graphs of finite groups and some theorems of Brandl-Shi type as their applications.
  

• 4:10 pm - 4:35 pm
  Name : Jumela Sarmiento
  Affiliation : Department of Mathematics, Kyushu University
  Title : Construction of flag-transitive designs with line size 4
  Abstract :
  

• 4:40 pm - 5:05 pm
  Name : Ma. Louise Antonette de Las Penas
  Affiliation : Department of Mathematics, Ateneo de Manila University, JSPS Research Fellow at Sophia University
  Titile : Analysis of colored symmetrical patterns
  Abstract : A method is presented for determining all colorings of a symmetrical structure for which the elements of a given subgroup H of the symmetry group G of the structure permute the colors and the elements of a given subgroup K of G fix the colors. The method is the applied to some special cases, for instance, the case where the index of H in G is a prime number p. Illustrations are given for colorings for plane crystallographic patterns.
  

Wednesday, December 16, 1998

• 10:00 am - 11:00 am
  Name : Hiro-Fumi Yamada, 山田裕史
  Affiliation : Department of Mathematics, Hokkaido University
  Title : Schur's Q-functions and affine Lie algebras
  Abstract : This talk deals with the weight vectors of the basic representations of the twisted affine Lie algebra of type D⁽²⁾_l+1. The weight vectors are expressed in terms of Schur's Q-functions. The up and down motion along a string of the fundamental imaginary root is described as a combinatorial game on an abacus. As a consequence one can determine the homogeneous polynomial solutions to the reduced BKP hierarchies as the maximal weight vectors. The results obtained will be applied to the case of A⁽¹⁾₁. The embedding of A⁽¹⁾₁ into D⁽²⁾₄ gives rise to a realization of the basic representation of A⁽¹⁾₁. The isomorphism between the "standard" and this "non-standard" realizations of the basic representation induces a "funny" identity of Schur's S-functions and Q-functions indexed by certain partitions. In fact this identity reflects a nature of decomposition matrices of the modular spin representations of the symmetric groups with characteristic 2.
  

• 11:10 am - 12:00 am
  Name : Hideak Morita, 森田英章
  Affiliation : Department of Mathematics, Department of Mathematics, Hokkaido University
  Title : On the Robinson-Schensted correspondence
  Abstract : We introduce a simple tableaux game which produces an element of symmetric groups from a pair of standard Young tableaux of same shape, and see that it coincides with the Robinson-Schensted correspondence in some special case.
  

• Lunch Time

• 1:30 pm - 2:00 pm
  Name : Hitoshi Kaneta, 兼田 均
  Affiliation : College of Engineering, Osaka Prefecture University
  Title : The most symmetric non-singular plane curves of degree n<8
  Abstract : We call a non-singualr plane algebraic curve f of degree n the most symmetric if the projective automorphism group Aut(f) has the greatest order among non-singualr plane algebraic curves of degree n. As n varies from 3 to 7, the most symmetric curves of degree n are projectively equivalent to

  x³+y³+z³, x³y+y³z+z³x, x⁵+y⁵+z⁵,
  10x³y³+9z(x⁵+y⁵)-45z²x²y²-135z⁴xy+27z⁶,
  and x⁷+y⁷+z⁷.

  
  

• 2:10 pm - 2:50 pm
  Name : Akira Hiraki, 平木彰
  Affiliation : Department of Mathematical Sciences, Osaka Kyoiku University
  Title : Strongly closed subgraphs in a distance-regular graph
  Abstract :
  

• 3:00 pm - 3:25 pm
  Name : Izumi Miyamoto, 宮本泉, (with Akihide Hanaki (Shinshu Univ.))
  Affiliation : Department of Mathematics, Yanamashi University
  Title : Computation of primitive association schemes with small number of vertices
  Abstract : All primitive association schemes with up to 22 vertices and all commutative association schemes with 23 vertices are computed.
  

• 3:30 pm - 3:55 pm
  Name : Mariko Hagita, 萩田 真理子
  Affiliation : Department of Mathematics, Faculty of Science and Technology, Keio University (Graduate School)
  Title : Folding maps in group rings
  Abstract : We make a map from an abelian group to another abelian group with the same order which holds some combinatorial relations
  

• 4:10 pm - 5:00 pm
  Name : Hiroshi Suzuki, 鈴木寛
  Affiliation : Department of Mathematics, International Christian University
  Title : On balanced sets and related structures
  Abstract :