Workshop on Algebraic Combinatorics 2011代数组合论国际学术会议 September 15-18, 2011 Organizers Eiichi Bannai Shanghai Jiao Tong University Suogang Gao Hebei Normal University Jun Ma Shanghai Jiao Tong University Kaishun Wang Beijing Normal University Yaokun Wu Shanghai Jiao Tong University Xiao-Dong Zhang Shanghai Jiao Tong University Department of Mathematics 上海交通大学数学系 Contents Welcome ........................................ 1 Program ........................................ 2 Abstracts ........................................ 6 List of Participants .................................. 34 Index of Speakers ................................... 37 Minhang Campus Map ............................... 38 Shanghai Metro Map ................................ 39 Welcome You are very much welcome to our Workshop on Algebraic Combinatorics at Shanghai Jiao Tong University. The workshop will take place from Sept. 15 to Sept. 18 and will be housed in the mathe- matics building of Shanghai Jiao Tong University. The scienti¯c program will consist of ten lectures of 50 minutes, thirty-three lectures of 30 minutes and ten lectures of 10 minutes. All 10 minutes speakers will have the chance to give another 30 minutes presentation in our satellite seminar on Sept. 19. There is basically no cost and no budget. But we believe that you can ¯nd in our work- shop lots of beautiful mathematical theorems and structures. There are even no conference badges. But we hope that you can get to know many mathematical good friends via their mathematics. We will provide all participants and accompanying persons modest lunches in university canteen. All of you are also invited to a conference banquet on the night of Sept. 16. Please come early to register to the lunches/banquet on the conference venue and take the lunch/banquet tickets { this helps us estimate the number of seats to be reserved in the canteen/restaurant. Although we have a dense schedule for mathematics in the south-west corner of Shang- hai, we wish that you can still ¯nd some time to do a wonderful city tour here, especially, considering that Shanghai Tourism Festival 2011 will last from this Sept. 10 to Oct. 6. When preparing your trip to Shanghai, it may be useful to observe the weather broadcast here: http://news.bbc.co.uk/weather/forecast/1713 Please do not hesitate to contact us for any possible help. We thank you for coming to our workshop and we wish you a good memory here. Workshop Organizers: Eiichi Bannai Shanghai Jiao Tong University Suogang Gao Hebei Normal University Jun Ma Shanghai Jiao Tong University Kaishun Wang Beijing Normal University Yaokun Wu Shanghai Jiao Tong University Xiao-Dong Zhang Shanghai Jiao Tong University 1 Program William J. Martin (Worcester Polytechnic Institute) Chair: 9:00- Sept. 15 Some Problems in the Theory of Q-Polynomial Association Eiichi Bannai 9:50 Schemes Chair: 10:00- Jianmin Ma (Hebei Normal University) Tatsuro Ito 10:50 Skew-Symmetric Association Schemes Chair: 11:00- Akihiro Munemasa (Tohoku University) Rongquan Feng 11:50 Frames of the Leech Lattice 11:50-13:20 Lunch Chair: 13:30- Mitsugu Hirasaka (Pusan National University) Sept. 15 Yoshiaki Itoh 14:00 Construction of Algebraically Isomorphic Association Schemes 14:00- Sho Suda (Tohoku University) 14:30 New Parameters of Subsets in Polynomial Association Schemes Chair: 14:40- Yuqun Chen (South China Normal University) Tongsuo Wu 15:10 GrÄobner-Shirshov Bases and PBW Theorems Wei Wang (Xi'an Jiaotong University) 15:10- Generalized Characteristic Polynomials and Generalized 15:40 GM-Switchings of Graphs Chair: 15:50- Jeong Rye Park (Pusan National University) Mitsugu Hirasaka 16:20 On 3-Equivalenced Association Scheme Nobuo Nakagawa (Kobe Gakuin University) 16:20- On Non-Isomorphism Problems of Strongly Regular Graphs 16:50 Constructed by p-ary Bent Functions Chair: 17:00- Yi-Huang Shen (University of Science and Technology of China) Yuqun Chen 17:30 Stanley Decompositions of Monomial Ideals Cuipo Jiang (Shanghai Jiao Tong University) 17:30- On Classi¯cation of Rational Vertex Operator Algebras 18:00 of Central Charge 1 2 Keqin Feng (Tsinghua University) Chair: 9:00- Sept. 16 Cyclotomic Constructions on Codebooks, MUB's, SIC-POVM 's Hao Shen 9:50 and Sphere t-Designs 9:50- Aixian Zhang (Capital Normal University) 10:00 Cyclotomic Constructions of Codebooks Tatsuro Ito (Kanazawa University) Chair: 10:10- Finite Dimensional Irreducible Representations of Certain Jacobus Koolen 11:00 Subalgebras of the Quantum A±ne Algebra Uq(slb 2) Hiroshi Nozaki (Tohoku University) Chair: 11:10- A Characterization of Strongly Regular Graphs from Euclidean Yi-Huang Shen 11:40 Representations of Graphs 11:40-13:20 Lunch Hao Shen (Shanghai Jiao Tong University) Chair: 13:30- Sept. 16 Resolvable Group Divisible Designs and (k; r)-Colorings of Beifang Chen 14:00 Complete Graphs 14:00- Hyonju Yu (Pohang University of Science and Technology) 14:30 Some Construction of Regular Graphs Chair: 14:40- Takuya Ikuta (Kobe Gakuin University) William J. Martin 15:10 Nomura Algebras of Nonsymmetric Hadamard Models 15:10- Koichi Betsumiya (Hirosaki University) 15:40 Even Self-dual Codes Over GF(4) Chair: 15:50- Yoshiaki Itoh (Institute of Statistical Mathematics) Jiayu Shao 16:20 Random Sequential Packing of Cubes Shun'ichi Yokoyama (Kyushu University) 16:20- Sage: Unifying Monstrous Moonshine, Modular Functions and 16:50 Mathematical Softwares Houyi Yu (Shanghai Jiaotong University) 16:50- Commutative Rings R Whose C(AG(R)) Only Consist of 17:00 Triangles Takayuki Okuda (University of Tokyo) Chair: 17:10- An Analogue of Fisher Type Inequality on Compact Symmetric Yaokun Wu 17:40 Spaces 17:40- Ziqing Xiang (Shanghai Jiao Tong University) 17:50 Fisher Type Inequality for Boolean Designs Eiichi Bannai (Shanghai Jiao Tong University) 17:50- Some Open Problems on Various Concepts of t-Designs and 18:00 Fisher Type Inequalities 18:30- The Workshop Banquet 3 Beifang Chen (Hong Kong University of Science and Technology) Chair: 9:00- Sept. 17 Lattice Polytopes, Ehrhart Polynomials, and Tutte Like Akihiro Higashitani 9:50 Polynomials Associated with Graphs Chair: 10:00- Jun Ma (Shanghai Jiao Tong University) Yoshihiro Mizoguchi 10:50 Tutte Polynomial and G-Parking Functions Chair: 11:00- Rongquan Feng (Peking University) Xiaodong Zhang 11:50 On the Coverings of Graphs 11:50-13:20 Lunch Chair: 13:30- Teruhisa Kadokami (East China Normal University) Sept. 17 Yuehui Zhang 14:00 Amphicheirality of Links and Alexander Invariants Akihiro Higashitani (Osaka University) 14:00- Roots of Ehrhart Polynomials of Reflexive Polytopes Arising 14:30 from Graphs Chair: 14:40- Chie Nara (Tokai University) Kaishun Wang 15:10 Flat Foldings of Convex Polyhedra 15:10- Tao Feng (Zhejiang University) 15:40 Recent Progress on Skew Hadarmard Di®erence Sets Chair: 15:50- Yoshihiro Mizoguchi (Kyushu University) Qiaoliang Li 16:20 Generalization of Compositions of Cellular Automata On Groups Prabhu Manyem (Shanghai University) 16:20- Optimization Problems and Universal Horn Formulae in 16:50 Existential Second Order Logic Chair: 17:00- Jun Guo (Langfang Teachers' College) Tao Feng 17:30 An ErdÄos-Ko-RadoTheorem in General Linear Groups Yaokun Wu (Shanghai Jiao Tong University) 17:30- Lit-Only σ-game On a Connected Graph with At Least 17:40 One Loop Yun-Ping Deng (Shanghai Jiao Tong University) 17:40- Maximum-Size Independent Sets and Automorphism Groups of 17:50 Tensor Powers of the Even Derangement Graphs Kyoung-Tark Kim (Pusan National University) 17:50- On Decompositions of Special Linear Algebras Over a Field of 18:00 Positive Characteristic 4 Chair: 9:00- Jacobus Koolen (Pohang University of Science and Technology) Sept. 18 Akihiro Munemasa 9:50 On Connectivity Problems in Distance-Regular Graphs Chair: 10:00- Xavier Dahan (Ky^ush^uUniversity) Keqin Feng 10:50 Ramanujan Graphs of Very Large Girth Based on Octonions Hirotake Kurihara (Tohoku University) Chair: 11:00- On the Character Tables of Some Association Schemes Based on Suogang Gao 11:30 t-Singular Linear Spaces 11:30- Kaishun Wang (Beijing Normal University) 12:00 A New Model for Pooling Designs 12:00-13:20 Lunch Chair: 13:30- Jongyook Park (Pohang University of Science and Technology) Sept. 18 Jianmin Ma 14:00 On the Parameters of a Distance-Regular Graph Xiao-Dong Zhang (Shanghai Jiao Tong University) 14:00- The Signless Laplacian Spectral Radii of Graphs with Given 14:30 Degree Sequences 14:30- Tetsuji Taniguchi (Matsue College of Technology) 15:00 On Fat Ho®man Graphs with Smallest Eigenvalue At Least ¡3 Guofu Yu (Shanghai Jiao Tong University) Chair: 15:10- Blaszak-Marciniak Lattice, Toda Lattice and Combinatorial Jun Ma 15:40 Numbers Stefan GrÄunewald (CAS-MPG Partner Institute for 15:40- Computational Biology) 16:10 On Agreement Forests Yoshio Sano (National Institute of Informatics) Chair: 16:20- The Competition Number of a Graph and the Holes in Stefan GrÄunewald 16:50 the Graph 16:50- Jeongmi Park (Pusan National University) 17:20 The Niche Graphs of Interval Orders Chair: 17:30- Peng Li (Shanghai Jiao Tong University) Tetsuji Taniguchi 17:40 A Four Sweep LBFS Algorithm for Recognizing Interval Graphs 17:40- Xiaomei Chen (Harbin Institute of Technology) 17:50 On Invariants of Digraphs Yangjing Long (Max Planck Institute for Mathematics in the 17:50- Sciences) 18:00 Relations Between Graphs 18:00- Simone Severini (University College London) 18:30 A Role for the Lovasz theta Function in Quantum Mechanics 5 Abstracts Sept. 15, 9:00 { 9:50 William J. Martin Some Problems in the Theory of Q-Polynomial Association Schemes William J. Martin Worcester Polytechnic Institute Email: [email protected] Q-polynomial, or \cometric", association schemes were de¯ned in 1973. Perhaps the most important examples are the classical distance-regular graphs. Up until 1998, very little was known about Q- polynomial schemes which are not also P -polynomial. With two fundamental papers of H. Suzuki, that changed. The last decade has seen a flurry of activity in this area. Many new examples have been found, including the ¯rst known in¯nite family of primitive Q-polynomial schemes which are neither P - polynomial nor duals of P -polynomial schemes.