Publications (or in press)

    1. Ehrhart quasi-polynomials and parallel translations (with S. Murai and M. Yoshinaga),
      Combinatorial Theory,, to appear.

    2. Examples and counterexamples in Ehrhart theory (with L. Ferroni),
      EMS Surv. Math. Sci., to appear.

    3. The h-vectors of edge rings of odd-cycle compositions (with K. Bhaskara and N. Shibu Deepthi),
      J. Algebra Appl., to appear.

    4. Generalized Alexander quandles of finite groups and their characterizations (with H. Kurihara),
      European J. Math., 10 no. 3, (2024).

    5. Difference of Hilbert series of homogeneous monoid algebras and their normalizations,
      Semigroup Forum, 108 (2024), 101--114.

    6. Combinatorial Mutations of Gelfand-Tsetlin Polytopes, Feigin-Fourier-Littelmann-Vinberg Polytopes, and Block Diagonal Matching Field Polytopes (with O. Clarke and F. Mohammadi),
      J. Pure Appl. Algebra, 228 no. 7, (2024), 107637.

    7. Feedback game on 3-chromatic Eulerian triangulations of surfaces (with K. Kurimoto and N. Matsumoto),
      Discrete Appl. Math., 347 (2024), 30--38.

    8. Kempe equivalence of almost bipartite graphs (with N. Matsumoto),
      Australas. J. Combin., 87 (2023), 203--213.

    9. The h-vectors of the edge rings of a special family of graphs (with N. Shibu Deepthi),
      Comm. Algebra, 51 (2023), 5287--5296.

    10. Combinatorial classification of (±1)-skew projective spaces (with K. Ueyama),
      Q. J. Math., 74 (2023), 939--956.

    11. The distribution of roots of Ehrhart polynomials for the dual of root polytopes (with Y. Yamada),
      Graphs and Comb., 39 (2023), 83.

    12. Adjacency matrices over a finite prime field and their direct sum decompositions (with Y. Sugishita),
      Linear Algebra Appl., 677 (15) (2023), 306--322.

    13. The equivariant Ehrhart theory of polytopes with order-two symmetries (with O. Clarke and M. Kölbl),
      Proc. Amer. Math. Soc., 151 (9) (2023), 4027--4041.

    14. Period collapse in characteristic quasi-polynomials of non-central hyperplane arrangements (with T. N. Tran and M. Yoshinaga),
      Int. Math. Res. Not. IMRN, 10 (2023), 8934--8963.

    15. Behaviors of pairs of dimensions and depths of edge ideals (with A. Kanno and R. Ueji),
      Comm. Algebra, 51 (8) (2023), 3574--3584.

    16. Combinatorial mutations of Newton-Okounkov polytopes arising from plabic graphs (with Y. Nakajima),
      Advanced Studies in Pure Mathematics, the proceeding of the conference "The McKay correspondence, mutation and related topics", Vol. 88., 2023. 227--278.

    17. Homogeneous quandles arising from automorphisms of symmetric groups (with H. Kurihara),
      Comm. Algebra, 51 (4) (2023), 1413--1430.

    18. The ratio of the numbers of odd and even cycles in outerplanar graphs (with. N. Matsumoto),
      Discrete Math., 346 (4) (2023), 113285.

    19. The characterisation problem of Ehrhart polynomials of lattice polytopes,
      Interactions with lattice polytopes, Springer Proc. Math. Stat., 386 (2022), 181–-195.

    20. The root distributions of Ehrhart polynomials of free sums of reflexive polytopes (with M. Hachimori and Y. Yamada),
      Electron. J. Combin., 29 (3) (2022), 1--17.

    21. Cohomological rigidity for Fano Bott manifolds (with K. Kurimoto),
      Math. Z., 301 (2022), 2369-–2391.

    22. Combinatorial Mutations and Block Diagonal Polytopes (with O. Clarke and F. Mohammadi),
      Collect. Math., 73 (2022), 305--335.

    23. Levelness versus almost Gorensteinness of edge rings of complete multipartite graphs (with K. Matsushita),
      Comm. Algebra, 50 no. 6, (2022), 2637--2652.

    24. Deformations of dimer models (with Y. Nakajima),
      SIGMA Symmetry Integrability Geom. Methods Appl., 18 (2022), 030, 53 pages.

    25. Three families of toric rings arising from posets or graphs with small class groups (with K. Matsushita),
      J. Pure Appl. Algebra, 226 no. 10, (2022), 107979.

    26. Inequalities of invariants on Stanley-Reisner rings of Cohen--Macaulay simplicial complexes (with H. Kanno and K. Matsuda),
      J. Pure Appl. Algebra, 226 no. 7, (2022), 106888.

    27. Cohomological rigidity for toric Fano manifolds of small dimensions or large Picard numbers (with K. Kurimoto and M. Masuda),
      Osaka J. Math., 59 (2022), 177--215.

    28. Combinatorial study of stable categories of graded Cohen-Macauly modules over skew quadric hypersufaces (with K. Ueyama),
      Collect. Math., 73 (2022), 43--54.

    29. Conic divisorial ideals and non-commutative crepant resolutions of edge rings of complete multipartite graphs (with K. Matsushita),
      J. Alg., 594 (2022), 685--711.

    30. Quadratic Gröbner bases of block diagonal matching field ideals and toric degenerations of Grassmannians (with H. Ohsugi),
      J. Pure Appl. Algebra, 226 no. 2, (2022), 106821.

    31. Gorenstein polytopes with trinomial h*-polynomials (with B. Nill and A. Tsuchiya),
      Beiträge zur Algebra und Geometrie, 62 (2021), 667--685.

    32. Newton-Okounkov bodies of flag varieties and combinatorial mutations (with N. Fujita),
      Int. Math. Res. Not. IMRN, no.12, (2021), 9567--9607.

    33. Winding Number of r-modular sequences and Applications to the Singularity Content of a Fano Polygon (with D. Cavey),
      Tohoku Math. J., 73 no.1, (2021), 137--158.

    34. Generalized F-signatures of Hibi rings (with Y. Nakajima),
      Illinois J. Math., 65 no.1, (2021), 97--120.

    35. Universal conditions on h*-vectors of lattice simplices,
      J. Geometry, 112 no.1, (2021), 9 pages.

    36. Toric ideals of Minkowski sums of unit simplices (with H. Ohsugi),
      Alg. Comb., 3 no. 4, (2020), 831--837.

    37. Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions (with Y. Nakajima),
      Selecta Math.(N.S.), 25 No. 78, (2019), 25 pages.

    38. Distribution of accumulation points of roots for type (n-1,1) Coxeter groups (with R. Mineyama and N. Nakashima),
      Nagoya Math. J., 235 (2019), 125--157.

    39. Smooth centrally symmetric polytopes in dimension 3 are IDP (with M. Beck, C. Haase, J. Hofscheier, K. Jochemko, L. Katthän and M. Michalek),
      Ann. Comb., 23 (2019), 255--262.

    40. Permutations with small maximal k-consecutive sums (with K. Kurimoto),
      Discrete Math., 342 (2019), 2467--2481.

    41. Arithmetic Aspects of symmetric edge polytopes (with K. Jochemko and M. Michalek),
      Mathematika, 65 (2019), 763--784.

    42. Unimodality on δ-vectors of lattice polytopes and two related properties,
      European J. Math., 5 (2019), 333--355.

    43. Lattice simplices of maximal dimension with a given degree,
      Michigan Math. J., 68 (2019), 193--210.

    44. Ehrhart Polynomial Roots of Reflexive Polytopes (with G. Hegedüs and A. Kasprzyk),
      Electron. J. Combin., 26 (2019), 1--27.

    45. Ehrhart polynomials with negative coefficients (with T. Hibi, A. Tsuchiya and K. Yoshida),
      Graphs and Comb., 35 (2019), 363--371.

    46. Universal inequalities in Ehrhart Theory (with G. Balletti),
      Israel J. Math., 227 (2018), 843--859.

    47. Existence of regular unimodular triangulations of dilated empty simplices (with T. Hibi and K. Yoshida),
      European J. Combin., 70 (2018), 374--383.

    48. Non-level semi-standard graded Cohen--Macaulay domain with h-vector (h0, h1, h2) (with K. Yanagawa),
      J. Pure Appl. Algebra, 222 (2018), 191--201.

    49. Lattice multipolygons (with M. Masuda),
      Kyoto J. Math., 57 (2017), 807--828.

    50. Interlacing Ehrhart Polynomials of Reflexive Polytopes (with M. Kummer and M. Michalek),
      Selecta Math., 23 (2017), 2977--2998.

    51. Integer decomposition property of free sums of convex polytopes (with T. Hibi),
      Ann. Comb., 20 (2016), 601--607.

    52. Minkowski sum of polytopes and its normality,
      J. Math. Soc. Japan., 68 (2016), 1147--1159.

    53. Almost Gorenstein homogeneous rings and their h-vectors,
      J. Alg., 456 (2016), 190--206.

    54. Dominating induced matchings of finite graphs and regularity of edge ideals (with T. Hibi, K. Kimura and A. Tsuchiya),
      J. Algebr. Comb., 43 (2016), 173--198.

    55. Smooth Fano polytopes arising from finite directed graphs,
      Kyoto J. Math., 55 (2015), 579--592.

    56. Algebraic study on Cameron-Walker graphs (with T. Hibi, K. Kimura and A. B. O'Keefe),
      J. Alg., 422 (2015), 257--269.

    57. Toric rings arising from cyclic polytopes (with T. Hibi, L. Katthän and R. Okazaki),
      Comm. Algebra, 43 (2015), 778--794.

    58. Non-normal very ample polytopes and their holes,
      Electron. J. Combin., 21 (2014), 1--12.

    59. Ehrhart polynomials of integral simplices with prime volumes,
      INTEGERS, 14 (2014), 1--15.

    60. Integer decomposition property of dilated polytopes (with D. A. Cox, C. Haase and T. Hibi),
      Electron. J. Combin., 21 (2014), 1--17.

    61. Depth of initial ideals of normal edge rings (with T. Hibi, K. Kimura and A. B. O'Keefe),
      Comm. Algebra, 42 (2014), 2908--2922.

    62. Normal cyclic polytopes and cyclic polytopes that are not very ample (with T. Hibi, L. Katthän and R. Okazaki),
      J. Australian Math. Soc., 96 (2014), 61--77.

    63. Hermite normal forms and δ-vector (with T. Hibi and N. Li),
      J. Comb. Theory Ser. A 119 (2012), 1158--1173.

    64. Counterexamples of the conjecture on roots of Ehrhart polynomials,
      Discrete Comput. Geom. 47 (2012), 618--623.

    65. Roots of Ehrhart polynomials arising from graphs (with T. Matsui, Y. Nagazawa, H. Ohsugi and T. Hibi),
      J. Algebr. Comb. 34 (2011), 721--749.

    66. Depth of edge rings arising from finite graphs (with T. Hibi, K. Kimura and A. B. O'Keefe),
      Proc. Amer. Math. Soc. 139 (2011), 3807--3813.

    67. Roots of Ehrhart polynomials of Gorenstein Fano polytopes (with T. Hibi and H. Ohsugi),
      Proc. Amer. Math. Soc. 139 (2011), 3727--3734.

    68. Smooth Fano polytopes arising from finite partially ordered sets (with T. Hibi),
      Discrete Comput. Geom. 45 (2011), 449--461.

    69. Ehrhart polynomials of convex polytopes with small volumes (with T. Hibi and Y. Nagazawa),
      European J. Combin. 32 (2011), 226--232.

    70. Shifted symmetric δ-vectors of convex polytopes,
      Discrete Math. 310 (2010), 2925--2934.

    Preprints (submitted)
    1. Binomial edge rings of complete bipartite graphs
    2. Combinatorics of graded module categories over skew polynomial algebras at roots of unity (with K. Ueyama)
    3. Classification of generalized Alexander quandles (with S. Kamada, J. Kosaka and H. Kurihara)
    4. Characteristic quasi-polynomials of deletions of Shi arrangements of type B and their period collapse (with N. Nakashima)
    5. Non-finitely generated monoids corresponding to finitely generated homogeneous subalgebras (with K. Tani)
    6. On the Ehrhart Theory of Generalized Symmetric Edge Polytopes (with R. Davis and H. Ohsugi)
    7. Fans and polytopes in tilting theory II: g-fans of rank 2 (with T. Aoki, O. Iyama, R. Kase and Y. Mizuno)
    8. Restricted Chain-Order Polytopes via Combinatorial Mutations (with O. Clarke and F. Zaffalon)
    9. Fans and polytopes in tilting theory I: Foundations (with T. Aoki, O. Iyama, R. Kase and Y. Mizuno)
    10. Two poset polytopes are mutation-equivalent

    Publications (Japanese)
    1. 『グレブナー教室 --計算代数統計への招待--』
      竹村彰道・日比孝之・原尚幸・東谷章弘・清智也・「グレブナー道場」著者一同 著（東谷は第５章を担当）、共立出版

    2. 『鏡映の数学 --有限鏡映群の幾何学--』
      小林雅人・陶山大輔・塚本靖之・中島規博・東谷章弘・嶺山良介 訳（東谷は第Ⅲ部を担当）、丸善出版
      原著："Mirrors and Reflections --The Geometry of Finite Reflection Groups--" by A. V. Borovik and A. Borovik