Hajime Tanaka

Publications/Preprints

See also my Google Scholar Citations and a list of my articles on arXiv.

My coauthors are: Eiichi Bannai (7), Etsuko Bannai (4), Renato Portugal (3), Mohamed Sabri (3), Sho Suda (3), Gen Kimura (2), Jack Koolen (2), Bill Martin (2), John Vincent Morales (2), Nobuaki Obata (2), Masanao Ozawa (2), Osamu Shimabukuro (2), Tao Wang (2), Yan Zhu (2), Edwin van Dam, Evangelos Georgiadis, Dion Gijswijt, Ferdinand Ihringer, Masoumeh Koohestani, Chin-Yen Lee, Jae-Ho Lee, Woo Sun Lee, Xiaoye Liang, Pedro Lugão, Hiroshi Mizukawa, Akihiro Munemasa, Lex Schrijver, Ying-Ying Tan, Rie Tanaka, Norihide Tokushige, Wei-Hsuan Yu.

  1. Characterizing graphs with fully positive semidefinite $\boldsymbol{Q}$-matrices
    H. Tanaka
    preprint (6pp.).
    arXiv:2208.11002
  2. Multimarked spatial search by continuous-time quantum walk
    P. H. G. Lugão, R. Portugal, M. Sabri, H. Tanaka
    preprint (18pp.)
    arXiv:2203.14384
  3. The real equiangular tight frames obtained from rank $\boldsymbol{3}$ graphs
    E. Bannai, E. Bannai, C.-Y. Lee, H. Tanaka, W.-H. Yu
    preprint (11pp.)
    arXiv:2202.09858
  4. Spatial search on Johnson graphs by discrete-time quantum walk
    H. Tanaka, M. Sabri, R. Portugal
    J. Phys. A 55 (2022) 255304 (16pp.)
    arXiv:2112.03744
  5. Tight relative $\boldsymbol{t}$-designs on two shells in hypercubes, and Hahn and Hermite polynomials
    E. Bannai, E. Bannai, H. Tanaka, Y. Zhu
    Ars Math. Contemp. 22 (2022) #P2.01 (43pp.)
    arXiv:2006.02054
  6. Spatial search on Johnson graphs by continuous-time quantum walk
    H. Tanaka, M. Sabri, R. Portugal
    Quantum Inf. Process. 21 (2022) 74 (13pp.) [SharedIt]
    arXiv:2108.01992
  7. A duality of scaffolds for translation association schemes
    X. Liang, Y.-Y. Tan, H. Tanaka, T. Wang
    Linear Algebra Appl. 638 (2022) 110–124
    arXiv:2110.15848
  8. Scaling limits for the Gibbs states on distance-regular graphs with classical parameters
    M. Koohestani, N. Obata, H. Tanaka
    SIGMA Symmetry Integrability Geom. Methods Appl. 17 (2021) 104 (22pp.)
    arXiv:2106.14497
  9. The Terwilliger algebra of the twisted Grassmann graph: the thin case
    H. Tanaka, T. Wang
    Electron. J. Combin. 28 (2020) #P4.15 (22pp.)
    arXiv:2009.09375
  10. Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier–Hermite polynomials
    J. V. S. Morales, N. Obata, H. Tanaka
    Colloq. Math. 162 (2020) 1–22
    arXiv:1809.03761
  11. The independence number of the orthogonality graph in dimension $\boldsymbol{2^k}$
    F. Ihringer, H. Tanaka
    Combinatorica 39 (2019) 1425–1428 [SharedIt]
    arXiv:1901.04860
  12. An Assmus–Mattson theorem for codes over commutative association schemes
    J. V. S. Morales, H. Tanaka
    Des. Codes Cryptogr. 86 (2018) 1039–1062 [SharedIt]
    arXiv:1610.07334
    [Here is a Mathematica code which implements Supplement 3.6 to compute the scalar $\mu(S)$.]
  13. Dual polar graphs, a nil-DAHA of rank one, and non-symmetric dual $\boldsymbol{q}$-Krawtchouk polynomials
    J.-H. Lee, H. Tanaka
    SIGMA Symmetry Integrability Geom. Methods Appl. 14 (2018) 009 (27pp.)
    arXiv:1709.07825
  14. A semidefinite programming approach to a cross-intersection problem with measures
    S. Suda, H. Tanaka, N. Tokushige
    Math. Program. 166 (2017) 113–130 [SharedIt]
    arXiv:1504.00135
  15. Design theory from the viewpoint of algebraic combinatorics
    E. Bannai, E. Bannai, H. Tanaka, Y. Zhu
    Graphs Combin. 33 (2017) 1–41 [SharedIt]
  16. Distance-regular graphs
    E. R. van Dam, J. H. Koolen, H. Tanaka
    Electron. J. Combin. (2016) #DS22 (156pp.)
    arXiv:1410.6294
  17. Arithmetic completely regular codes
    J. H. Koolen, W. S. Lee, W. J. Martin, H. Tanaka
    Discrete Math. Theor. Comput. Sci. 17 (2016) 59–76
    arXiv:0911.1826
  18. On relative $\boldsymbol{t}$-designs in polynomial association schemes
    E. Bannai, E. Bannai, S. Suda, H. Tanaka
    Electron. J. Combin. 22 (2015) #P4.47 (17pp.)
    arXiv:1303.7163
  19. A cross-intersection theorem for vector spaces based on semidefinite programming
    S. Suda, H. Tanaka
    Bull. Lond. Math. Soc. 46 (2014) 342–348
    arXiv:1304.5466
  20. The Erdős–Ko–Rado basis for a Leonard system
    H. Tanaka
    Contrib. Discrete Math. 8 (2013) 41–59
    arXiv:1208.4050
  21. The Erdős–Ko–Rado theorem for twisted Grassmann graphs
    H. Tanaka
    Combinatorica 32 (2012) 735–740 [SharedIt]
    arXiv:1012.5692
  22. A note on super Catalan numbers
    E. Georgiadis, A. Munemasa, H. Tanaka
    Interdiscip. Inform. Sci. 18 (2012) 23–24
    arXiv:1101.1579
  23. Vertex subsets with minimal width and dual width in $\boldsymbol{Q}$-polynomial distance-regular graphs
    H. Tanaka
    Electron. J. Combin. 18 (2011) #P167 (32pp.)
    arXiv:1011.2000
  24. Nonexistence of exceptional imprimitive $\boldsymbol{Q}$-polynomial association schemes with six classes
    H. Tanaka, R. Tanaka
    European J. Combin. 32 (2011) 155–161
    arXiv:1005.3598
  25. Finite Euclidean graphs and Ramanujan graphs
    E. Bannai, O. Shimabukuro, H. Tanaka
    Discrete Math. 309 (2009) 6126–6134
  26. A bilinear form relating two Leonard systems
    H. Tanaka
    Linear Algebra Appl. 431 (2009) 1726–1739
    arXiv:0807.0385
    [I recommend looking at the arXiv version, rather than the published version.]
  27. Commutative association schemes
    W. J. Martin, H. Tanaka
    European J. Combin. 30 (2009) 1497–1525
    arXiv:0811.2475
  28. New proofs of the Assmus–Mattson theorem based on the Terwilliger algebra
    H. Tanaka
    European J. Combin. 30 (2009) 736–746
    arXiv:math/0612740
  29. A note on the span of Hadamard products of vectors
    H. Tanaka
    Linear Algebra Appl. 430 (2009) 865–867
    arXiv:0806.2075
  30. Comments on "Best conventional solutions to the King's problem"
    G. Kimura, H. Tanaka, M. Ozawa
    Z. Naturforsch. A 62a (2007) 152–156
    arXiv:quant-ph/0612053
  31. New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming
    D. Gijswijt, A. Schrijver, H. Tanaka
    J. Combin. Theory Ser. A 113 (2006) 1719–1731
  32. Classification of subsets with minimal width and dual width in Grassmann, bilinear forms and dual polar graphs
    H. Tanaka
    J. Combin. Theory Ser. A 113 (2006) 903–910
  33. Solution to the mean king's problem with mutually unbiased bases for arbitrary levels
    G. Kimura, H. Tanaka, M. Ozawa
    Phys. Rev. A 73 (2006) 050301(R) (4pp.)
    arXiv:quant-ph/0604096
  34. Association schemes of affine type over finite rings
    H. Tanaka
    Adv. Geom. 4 (2004) 241–261
  35. $\boldsymbol{(n+1,m+1)}$-hypergeometric functions associated to character algebras
    H. Mizukawa, H. Tanaka
    Proc. Amer. Math. Soc. 132 (2004) 2613–2618
  36. Finite analogues of non-Euclidean spaces and Ramanujan graphs
    E. Bannai, O. Shimabukuro, H. Tanaka
    European J. Combin. 25 (2004) 243–259
  37. The decomposition of the permutation character $\boldsymbol{1_{GL(n,q^2)}^{GL(2n,q)}}$
    E. Bannai, H. Tanaka
    J. Algebra 265 (2003) 496–512
  38. A four-class subscheme of the association scheme coming from the action of $\boldsymbol{PGL(2,4^f)}$
    H. Tanaka
    European J. Combin. 23 (2002) 121–129

Other manuscripts

  1. Dual polar graphs, a nil-DAHA of rank one, and non-symmetric dual $\boldsymbol{q}$-Krawtchouk polynomials (extended abstract)
    J.-H. Lee, H. Tanaka
    Proceedings of the 29th International Conference on "Formal Power Series and Algebraic Combinatorics", Queen Mary University of London, UK, Jul 9–13, 2017.
    Sém. Lothar. Combin. 78B (2017) #42 (12pp.)
  2. On some Gelfand pairs and commutative association schemes
    E. Bannai, H. Tanaka
    Jpn. J. Math. 10 (2015) 97–104 [SharedIt]
    Appendix of the following article:
    Mackey's theory of $\boldsymbol{\tau}$-conjugate representations for finite groups
    T. Ceccherini-Silberstein, F. Scarabotti, F. Tolli
    Jpn. J. Math. 10 (2015) 43–96
    arXiv:1311.7252
    [The original version of the appendix appeared in the unofficial proceedings, "Combinatorial Number Theory and Algebraic Combinatorics," Yamagata University, Yamagata, Japan, Nov 2002, pp. 1–8.]
  3. Group-case commutative association schemes and their character tables
    S. Y. Song, H. Tanaka
    arXiv:0809.0748
    [This manuscript appeared in the unofficial proceedings, "Algebraic Combinatorics, An International Conference in Honor of Eiichi Bannai's 60th Birthday," Sendai International Center, Sendai, Japan, Jun 2006, pp. 204–213.]
  4. PDF
    369KB
    On some relationships among the association schemes of finite orthogonal groups acting on hyperplanes
    H. Tanaka
    master thesis, Kyushu University, Mar 2001

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Selected Presentations

See also my researchmap portal for a more comprehensive list.

  1. PDF
    451KB
    Scaling limits for the Gibbs states on distance-regular graphs with classical parameters
    The 19th Workshop: Noncommutative Probability, Noncommutative Harmonic Analysis and Related Topics, with Applications
    Stefan Banach Conference Center, Będlewo, Poland (online)
    Aug 2022
  2. PDF
    360KB
    invited Spatial search on Johnson graphs by discrete-time quantum walk
    Workshop on Algebraic Combinatorics
    Academia Sinica, Taipei, Taiwan (online)
    Jan 2022
  3. PDF
    659KB
    invited Spatial search on Johnson graphs by continuous-time quantum walk
    Workshop on Algebraic Graph Theory and Quantum Information
    The Fields Institute, Toronto, Ontario, Canada (online)
    Aug 2021
  4. PDF
    291KB
    The independence number of the orthogonality graph in dimension $\boldsymbol{2^k}$
    Frontiers in Mathematical Science Research Workshop
    Shanghai University, Shanghai, China
    Sep 2019
  5. PDF
    841KB
    Tight relative $\boldsymbol{t}$-designs on two shells in hypercubes, and Hahn and Hermite polynomials
    Special Session on Association Schemes and Related Topics – in Celebration of J.D.H. Smith's 70th Birthday, AMS Fall Central Sectional Meeting
    University of Wisconsin–Madison, Madison, WI, USA
    Sep 2019
  6. PDF
    166KB
    invited Current progress in the Delsarte theory
    International Workshop on Algebraic Combinatorics
    Anhui University, Hefei, China
    Nov 2018
  7. PDF
    1.2MB
    Terwilliger
    (On a generalization of the Terwilliger algebra of a distance-regular graph)
    (The 63rd Algebra Symposium)
    Tokyo Institute of Technology, Tokyo, Japan
    Sep 2018
  8. PDF
    1.1MB
    invited Association schemes and orthogonal polynomials
    International Workshop on Bannai-Ito Theory
    Zhejiang University, Hangzhou, China
    Nov 2017
  9. PDF
    629KB
    On tight relative $\boldsymbol{t}$-designs in hypercubes
    Mini-Symposium: Hadamard Matrices and Combinatorial Designs, The Japanese Conference on Combinatorics and its Applications (JCCA 2016)
    Kyoto University, Kyoto, Japan
    May 2016
  10. PDF
    77KB
    A semidefinite programming approach to a cross-intersection problem with measures
    Systems of Lines: Applications of Algebraic Combinatorics
    Worcester Polytechnic Institute, Worcester, MA, USA
    Aug 2015
  11. PDF
    542KB
    invited The Terwilliger algebra of a $\boldsymbol{Q}$-polynomial distance-regular graph with respect to a set of vertices
    Algebraic Combinatorics Workshop
    University of Science and Technology of China, Hefei, China
    Nov 2014
  12. PDF
    294KB
    invited A cross-intersection theorem for vector spaces based on semidefinite programming
    8th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
    Pannon Egyetem, Veszprém, Hungary
    Jun 2013
  13. PDF
    229KB
    Extending the Erdős–Ko–Rado theorem
    2012 Shanghai Conference on Algebraic Combinatorics
    Shanghai Jiao Tong University, Shanghai, China
    Aug 2012
  14. PDF
    283KB
    Extending the Erdős–Ko–Rado theorem
    The 5th International Workshop on Optimal Network Topologies (IWONT 2012)
    Institut Teknologi Bandung, Bandung, Indonesia
    Jul 2012
  15. PDF
    457KB

    (Applications of semidefinite programming in Algebraic Combinatorics)
    (The 23rd RAMP Symposium)
    Kansai University, Suita, Japan
    Oct 2011
  16. PDF
    310KB
    Vertex subsets with minimal width and dual width in $\boldsymbol{Q}$-polynomial distance-regular graphs
    Geometric and Algebraic Combinatorics 5
    Hotel Conferentiecentrum Boschoord, Oisterwijk, The Netherlands
    Aug 2011
  17. PDF
    537KB
    Vertex subsets with minimal width and dual width in $\boldsymbol{Q}$-polynomial distance-regular graphs
    Linear Algebra Techniques in Combinatorics/Graph Theory
    The Banff Centre, Banff, Alberta, Canada
    Jan–Feb 2011
  18. Dual-tight cometric association schemes
    Special Session on Algebraic Graph Theory, Association Schemes, and Related Topics, AMS 2009 Spring Eastern Section Meeting
    Worcester Polytechnic Institute, Worcester, MA, USA
    Apr 2009
  19. PDF
    1MB
    A bilinear form relating two Leonard pairs and its applications
    Geometric and Algebraic Combinatorics 4
    Hotel Conferentiecentrum Boschoord, Oisterwijk, The Netherlands
    Aug 2008
  20. On subsets with minimal width and dual width in $\boldsymbol{Q}$-polynomial distance-regular graphs
    Bled’07, 6th Slovenian International Conference on Graph Theory
    Hotel Kompas Bled, Bled, Slovenia
    Jun 2007
  21. PDF
    577KB
    A strengthening of the Assmus–Mattson theorem based on the displacement and split decompositions
    CanaDAM 2007, 1st Canadian Discrete and Algorithmic Mathematics Conference
    The Banff Centre, Banff, Alberta, Canada
    May 2007
  22. Terwilliger
    (A semidefinite programming bound for codes based on the Terwilliger algebra)
    (The 51st Algebra Symposium)
    University of Tokyo, Tokyo, Japan
    Aug 2006
  23. A new proof of the Assmus–Mattson theorem based on the Terwilliger algebra
    Algebraic Combinatorics, An International Conference in Honor of Eiichi Bannai's 60th Birthday
    Sendai International Center, Sendai, Japan
    Jun 2006
  24. invited Classification of subsets with minimal width and dual width in Grassmann, bilinear forms and dual polar graphs
    The Fifth Shanghai Conference on Combinatorics
    Shanghai Jiao Tong University, Shanghai, China
    May 2005
  25. Schrijver bound for nonbinary codes
    COE Workshop on Sphere Packings
    Kyushu University, Fukuoka, Japan
    Nov 2004
  26. Character tables of commutative association schemes and coding theory
    Workshop 'Open Problems on Association Schemes'
    Pusan National University, Busan, Korea
    Jul 2004
  27. On eigenmatrices of certain character algebras and $\boldsymbol{(n+1,m+1)}$-hypergeometric functions
    The Second East Asian Conference on Algebra and Combinatorics
    Kyushu University, Fukuoka, Japan
    Nov 2003
  28. Association schemes of affine type over finite rings
    Conference on Algebra
    Ateneo de Manila University, Manila, The Philippines
    Dec 2002
  29. The decomposition of the permutation character $\boldsymbol{1_{GL(n,q^2)}^{GL(2n,q)}}$
    East Asian Conference on Algebra and Combinatorics
    Taiwan University, Taipei, Taiwan
    Sep 2001
  30. On some relationships among the association schemes of finite orthogonal groups acting on hyperplanes
    Com2MaC Conference on Association Schemes, Codes and Designs
    POSTECH, Pohang, Korea
    Jul 2000

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Some Past Events

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