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, ChinYen Lee, JaeHo Lee, Woo Sun Lee, Xiaoye Liang, Pedro Lugão, Hiroshi Mizukawa, Akihiro Munemasa, Lex Schrijver, YingYing Tan, Rie Tanaka, Norihide Tokushige, WeiHsuan Yu.
 Characterizing graphs with fully positive semidefinite $\boldsymbol{Q}$matrices
H. Tanaka
preprint (6pp.).
arXiv:2208.11002  Multimarked spatial search by continuoustime quantum walk
P. H. G. Lugão, R. Portugal, M. Sabri, H. Tanaka
preprint (18pp.)
arXiv:2203.14384  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  Spatial search on Johnson graphs by discretetime quantum walk
H. Tanaka, M. Sabri, R. Portugal
J. Phys. A 55 (2022) 255304 (16pp.)
arXiv:2112.03744  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  Spatial search on Johnson graphs by continuoustime quantum walk
H. Tanaka, M. Sabri, R. Portugal
Quantum Inf. Process. 21 (2022) 74 (13pp.) [SharedIt]
arXiv:2108.01992  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  Scaling limits for the Gibbs states on distanceregular graphs with classical parameters
M. Koohestani, N. Obata, H. Tanaka
SIGMA Symmetry Integrability Geom. Methods Appl. 17 (2021) 104 (22pp.)
arXiv:2106.14497  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  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  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  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 $\mu(S)$.]  Dual polar graphs, a nilDAHA of rank one, and nonsymmetric dual $\boldsymbol{q}$Krawtchouk polynomials
J.H. Lee, H. Tanaka
SIGMA Symmetry Integrability Geom. Methods Appl. 14 (2018) 009 (27pp.)
arXiv:1709.07825  A semidefinite programming approach to a crossintersection problem with measures
S. Suda, H. Tanaka, N. Tokushige
Math. Program. 166 (2017) 113–130 [SharedIt]
arXiv:1504.00135  Design theory from the viewpoint of algebraic combinatorics
E. Bannai, E. Bannai, H. Tanaka, Y. Zhu
Graphs Combin. 33 (2017) 1–41 [SharedIt]  Distanceregular graphs
E. R. van Dam, J. H. Koolen, H. Tanaka
Electron. J. Combin. (2016) #DS22 (156pp.)
arXiv:1410.6294  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  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  A crossintersection theorem for vector spaces based on semidefinite programming
S. Suda, H. Tanaka
Bull. Lond. Math. Soc. 46 (2014) 342–348
arXiv:1304.5466  The Erdős–Ko–Rado basis for a Leonard system
H. Tanaka
Contrib. Discrete Math. 8 (2013) 41–59
arXiv:1208.4050  The Erdős–Ko–Rado theorem for twisted Grassmann graphs
H. Tanaka
Combinatorica 32 (2012) 735–740 [SharedIt]
arXiv:1012.5692  A note on super Catalan numbers
E. Georgiadis, A. Munemasa, H. Tanaka
Interdiscip. Inform. Sci. 18 (2012) 23–24
arXiv:1101.1579  Vertex subsets with minimal width and dual width in $\boldsymbol{Q}$polynomial distanceregular graphs
H. Tanaka
Electron. J. Combin. 18 (2011) #P167 (32pp.)
arXiv:1011.2000  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  Finite Euclidean graphs and Ramanujan graphs
E. Bannai, O. Shimabukuro, H. Tanaka
Discrete Math. 309 (2009) 6126–6134  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.]  Commutative association schemes
W. J. Martin, H. Tanaka
European J. Combin. 30 (2009) 1497–1525
arXiv:0811.2475  New proofs of the Assmus–Mattson theorem based on the Terwilliger algebra
H. Tanaka
European J. Combin. 30 (2009) 736–746
arXiv:math/0612740  A note on the span of Hadamard products of vectors
H. Tanaka
Linear Algebra Appl. 430 (2009) 865–867
arXiv:0806.2075  Comments on "Best conventional solutions to the King's problem"
G. Kimura, H. Tanaka, M. Ozawa
Z. Naturforsch. A 62a (2007) 152–156
arXiv:quantph/0612053  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  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  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:quantph/0604096  Association schemes of affine type over finite rings
H. Tanaka
Adv. Geom. 4 (2004) 241–261  $\boldsymbol{(n+1,m+1)}$hypergeometric functions associated to character algebras
H. Mizukawa, H. Tanaka
Proc. Amer. Math. Soc. 132 (2004) 2613–2618  Finite analogues of nonEuclidean spaces and Ramanujan graphs
E. Bannai, O. Shimabukuro, H. Tanaka
European J. Combin. 25 (2004) 243–259  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  A fourclass 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
 Dual polar graphs, a nilDAHA of rank one, and nonsymmetric dual $\boldsymbol{q}$Krawtchouk polynomials (extended abstract)
J.H. Lee, H. Tanaka
Proceedings of the 29^{th} 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.)  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. CeccheriniSilberstein, 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.]  Groupcase 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.] 
On some relationships among the association schemes of finite orthogonal groups acting on hyperplanes
H. Tanaka
master thesis, Kyushu University, Mar 2001
Selected Presentations
See also my researchmap portal for a more comprehensive list.

Scaling limits for the Gibbs states on distanceregular 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 
invited
Spatial search on Johnson graphs by discretetime quantum walk
Workshop on Algebraic Combinatorics
Academia Sinica, Taipei, Taiwan (online)
Jan 2022 
invited
Spatial search on Johnson graphs by continuoustime quantum walk
Workshop on Algebraic Graph Theory and Quantum Information
The Fields Institute, Toronto, Ontario, Canada (online)
Aug 2021 
The independence number of the orthogonality graph in dimension $\boldsymbol{2^k}$
Frontiers in Mathematical Science Research Workshop
Shanghai University, Shanghai, China
Sep 2019 
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 
invited
Current progress in the Delsarte theory
International Workshop on Algebraic Combinatorics
Anhui University, Hefei, China
Nov 2018 
距離正則グラフの Terwilliger 代数の拡張について
(On a generalization of the Terwilliger algebra of a distanceregular graph)
第63回 代数学シンポジウム (The 63rd Algebra Symposium)
Tokyo Institute of Technology, Tokyo, Japan
Sep 2018 
invited
Association schemes and orthogonal polynomials
International Workshop on BannaiIto Theory
Zhejiang University, Hangzhou, China
Nov 2017 
On tight relative $\boldsymbol{t}$designs in hypercubes
MiniSymposium: Hadamard Matrices and Combinatorial Designs, The Japanese Conference on Combinatorics and its Applications (JCCA 2016)
Kyoto University, Kyoto, Japan
May 2016 
A semidefinite programming approach to a crossintersection problem with measures
Systems of Lines: Applications of Algebraic Combinatorics
Worcester Polytechnic Institute, Worcester, MA, USA
Aug 2015 
invited
The Terwilliger algebra of a $\boldsymbol{Q}$polynomial distanceregular graph with respect to a set of vertices
Algebraic Combinatorics Workshop
University of Science and Technology of China, Hefei, China
Nov 2014 
invited
A crossintersection theorem for vector spaces based on semidefinite programming
8th JapaneseHungarian Symposium on Discrete Mathematics and Its Applications
Pannon Egyetem, Veszprém, Hungary
Jun 2013 
Extending the Erdős–Ko–Rado theorem
2012 Shanghai Conference on Algebraic Combinatorics
Shanghai Jiao Tong University, Shanghai, China
Aug 2012 
Extending the Erdős–Ko–Rado theorem
The 5^{th} International Workshop on Optimal Network Topologies (IWONT 2012)
Institut Teknologi Bandung, Bandung, Indonesia
Jul 2012 
代数的組合せ論に於ける半正定値計画の応用
(Applications of semidefinite programming in Algebraic Combinatorics)
第23回RAMPシンポジウム (The 23rd RAMP Symposium)
Kansai University, Suita, Japan
Oct 2011 
Vertex subsets with minimal width and dual width in $\boldsymbol{Q}$polynomial distanceregular graphs
Geometric and Algebraic Combinatorics 5
Hotel Conferentiecentrum Boschoord, Oisterwijk, The Netherlands
Aug 2011 
Vertex subsets with minimal width and dual width in $\boldsymbol{Q}$polynomial distanceregular graphs
Linear Algebra Techniques in Combinatorics/Graph Theory
The Banff Centre, Banff, Alberta, Canada
Jan–Feb 2011  Dualtight 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 
A bilinear form relating two Leonard pairs and its applications
Geometric and Algebraic Combinatorics 4
Hotel Conferentiecentrum Boschoord, Oisterwijk, The Netherlands
Aug 2008  On subsets with minimal width and dual width in $\boldsymbol{Q}$polynomial distanceregular graphs
Bled’07, 6th Slovenian International Conference on Graph Theory
Hotel Kompas Bled, Bled, Slovenia
Jun 2007 
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  Terwilliger 代数に基づく符号の半正定値計画限界
(A semidefinite programming bound for codes based on the Terwilliger algebra)
第51回代数学シンポジウム (The 51st Algebra Symposium)
University of Tokyo, Tokyo, Japan
Aug 2006  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  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  Schrijver bound for nonbinary codes
COE Workshop on Sphere Packings
Kyushu University, Fukuoka, Japan
Nov 2004  Character tables of commutative association schemes and coding theory
Workshop 'Open Problems on Association Schemes'
Pusan National University, Busan, Korea
Jul 2004  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  Association schemes of affine type over finite rings
Conference on Algebra
Ateneo de Manila University, Manila, The Philippines
Dec 2002  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  On some relationships among the association schemes of ﬁnite orthogonal groups acting on hyperplanes
Com^{2}MaC Conference on Association Schemes, Codes and Designs
POSTECH, Pohang, Korea
Jul 2000
Some Past Events
 スペクトラルグラフ理論および周辺領域 第10回研究集会
(The 10^{th} Workshop on Spectral Graph Theory and Related Topics)
Nov 19–20, 2021
[This event took place virtually.]  スペクトラルグラフ理論および周辺領域 第9回研究集会
(The 9^{th} Workshop on Spectral Graph Theory and Related Topics)
Aug 18–20, 2020
[This event took place virtually.]  Sendai Workshop on Combinatorics
Tohoku University
Dec 2–4, 2019  スペクトラルグラフ理論および周辺領域 第8回研究集会
(The 8^{th} Workshop on Spectral Graph Theory and Related Topics)
National Institute of Technology, Miyakonojo College
Aug 27–29, 2019  スペクトラルグラフ理論および周辺領域 第7回研究集会
(The 7^{th} Workshop on Spectral Graph Theory and Related Topics)
Kitakyushu Municipal Gender Equality Center "Move"
Nov 14–16, 2018  The Japanese Conference on Combinatorics and its Applications (JCCA 2018)
Sendai International Center, Sendai
May 20–24, 2018  第3回代数的組合せ論 ｢仙台勉強会｣
(The Third Sendai Workshop on Algebraic Combinatorics)
Tohoku University
Mar 5–9, 2018  Hadamard Matrices and Their Applications
Tohoku University
Jan 26–27, 2018  スペクトラルグラフ理論および周辺領域 第6回研究集会
(The 6^{th} Workshop on Spectral Graph Theory and Related Topics)
Tottori University, Oct 14–15, 2017  第2回代数的組合せ論 ｢仙台勉強会｣
(The Second Sendai Workshop on Algebraic Combinatorics)
Tohoku University
Mar 7–8, 2017  スペクトラルグラフ理論および周辺領域 第5回研究集会
(The 5^{th} Workshop on Spectral Graph Theory and Related Topics)
Kobe University
Nov 26–27, 2016  ミニ集会 ｢代数的組合せ論とその周辺｣
(MiniWorkshop "Algebraic Combinatorics and Related Topics")
Tohoku University
Mar 8–9, 2016  スペクトラルグラフ理論および周辺領域 第4回研究集会
(The 4^{th} Workshop on Spectral Graph Theory and Related Topics) English program
University of Tsukuba
Nov 20–22, 2015  第1回代数的組合せ論 ｢仙台勉強会｣
(The First Sendai Workshop on Algebraic Combinatorics)
Tohoku University
May 8–9, 2015  スペクトラルグラフ理論および周辺領域 第3回研究集会
(The Third Workshop on Spectral Graph Theory and Related Topics) English program
Hiroshima Institute of Technology
Mar 13–15, 2015  RIMS研究集会 ｢有限群とその表現, 頂点作用素代数, 代数的組合せ論の研究｣
(RIMS Workshop: "Research on Finite Groups and Their Representations, Vertex Operator Algebras, and Algebraic Combinatorics") English program
Research Institute for Mathematical Sciences, Kyoto University
Dec 16–19, 2014  第31回代数的組合せ論シンポジウム
(The 31^{st} Algebraic Combinatorics Symposium)
Tohoku University
Jun 19–20, 2014  代数的組合せ論 ｢夏の学校 2014｣
(Algebraic Combinatorics Summer School 2014)
Akiu Resort Hotel Crescent, Sendai
Jun 15–18, 2014  The Second Workshop on Spectral Graph Theory and Related Topics
Tohoku University
Nov 29–30, 2013  International Workshop on Noncommutative Analysis and its Future Prospects
Hokkaido University
Aug 5–7, 2013  The 1st GSISRCPAM International Symposium
"Exploring New Frontiers of Pure and Applied Mathematics"
Tohoku University
Mar 8, 2013  The First Workshop on Algebraic Graph Theory, Spectral Graph Theory and Related Topics
Nagoya University
Jan 5–6, 2013  Schemes and Spheres
Worcester Polytechnic Institute, Worcester, MA, USA
May 24–28, 2010  Algebraic Combinatorics
An International Conference in Honor of Eiichi Bannai's 60th Birthday
Sendai International Center, Sendai
Jun 26–30, 2006