Publications (or in press)
- Examples and counterexamples in Ehrhart theory (with L. Ferroni),
EMS Surv. Math. Sci., to appear.
- The h-vectors of edge rings of odd-cycle compositions (with K. Bhaskara and N. Shibu Deepthi),
J. Algebra Appl., to appear.
- Generalized Alexander quandles of finite groups and their characterizations (with H. Kurihara),
European J. Math., 10 no. 3, (2024).
- Difference of Hilbert series of homogeneous monoid algebras and their normalizations,
Semigroup Forum, 108 (2024), 101--114.
- 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.
- Feedback game on 3-chromatic Eulerian triangulations of surfaces (with K. Kurimoto and N. Matsumoto),
Discrete Appl. Math., 347 (2024), 30--38.
- Kempe equivalence of almost bipartite graphs (with N. Matsumoto),
Australas. J. Combin., 87 (2023), 203--213.
- The h-vectors of the edge rings of a special family of graphs (with N. Shibu Deepthi),
Comm. Algebra, 51 (2023), 5287--5296.
- Combinatorial classification of (±1)-skew projective spaces (with K. Ueyama),
Q. J. Math., 74 (2023), 939--956.
- The distribution of roots of Ehrhart polynomials for the dual of root polytopes (with Y. Yamada),
Graphs and Comb., 39 (2023), 83.
- Adjacency matrices over a finite prime field and their direct sum decompositions (with Y. Sugishita),
Linear Algebra Appl., 677 (15) (2023), 306--322.
- 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.
- 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.
- Behaviors of pairs of dimensions and depths of edge ideals (with A. Kanno and R. Ueji),
Comm. Algebra, 51 (8) (2023), 3574--3584.
- 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.
- Homogeneous quandles arising from automorphisms of symmetric groups (with H. Kurihara),
Comm. Algebra, 51 (4) (2023), 1413--1430.
- The ratio of the numbers of odd and even cycles in outerplanar graphs (with. N. Matsumoto),
Discrete Math., 346 (4) (2023), 113285.
- The characterisation problem of Ehrhart polynomials of lattice polytopes,
Interactions with lattice polytopes, Springer Proc. Math. Stat., 386 (2022), 181–-195.
- 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.
- Cohomological rigidity for Fano Bott manifolds (with K. Kurimoto),
Math. Z., 301 (2022), 2369-–2391.
- Combinatorial Mutations and Block Diagonal Polytopes (with O. Clarke and F. Mohammadi),
Collect. Math., 73 (2022), 305--335.
- Levelness versus almost Gorensteinness of edge rings of complete multipartite graphs (with K. Matsushita),
Comm. Algebra, 50 no. 6, (2022), 2637--2652.
- Deformations of dimer models (with Y. Nakajima),
SIGMA Symmetry Integrability Geom. Methods Appl., 18 (2022), 030, 53 pages.
- 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.
- 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.
- 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.
- Combinatorial study of stable categories of graded Cohen-Macauly modules over skew quadric hypersufaces (with K. Ueyama),
Collect. Math., 73 (2022), 43--54.
- Conic divisorial ideals and non-commutative crepant resolutions of edge rings of complete multipartite graphs (with K. Matsushita),
J. Alg., 594 (2022), 685--711.
- 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.
- Gorenstein polytopes with trinomial h*-polynomials (with B. Nill and A. Tsuchiya),
Beiträge zur Algebra und Geometrie, 62 (2021), 667--685.
- Newton-Okounkov bodies of flag varieties and combinatorial mutations (with N. Fujita),
Int. Math. Res. Not. IMRN, no.12, (2021), 9567--9607.
- 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.
- Generalized F-signatures of Hibi rings (with Y. Nakajima),
Illinois J. Math., 65 no.1, (2021), 97--120.
- Universal conditions on h*-vectors of lattice simplices,
J. Geometry, 112 no.1, (2021), 9 pages.
- Toric ideals of Minkowski sums of unit simplices (with H. Ohsugi),
Alg. Comb., 3 no. 4, (2020), 831--837.
- 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.
- 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.
- 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.
- Permutations with small maximal k-consecutive sums (with K. Kurimoto),
Discrete Math., 342 (2019), 2467--2481.
- Arithmetic Aspects of symmetric edge polytopes (with K. Jochemko and M. Michalek),
Mathematika, 65 (2019), 763--784.
- Unimodality on δ-vectors of lattice polytopes and two related properties,
European J. Math., 5 (2019), 333--355.
- Lattice simplices of maximal dimension with a given degree,
Michigan Math. J., 68 (2019), 193--210.
- Ehrhart Polynomial Roots of Reflexive Polytopes (with G. Hegedüs and A. Kasprzyk),
Electron. J. Combin., 26 (2019), 1--27.
- Ehrhart polynomials with negative coefficients (with T. Hibi, A. Tsuchiya and K. Yoshida),
Graphs and Comb., 35 (2019), 363--371.
- Universal inequalities in Ehrhart Theory (with G. Balletti),
Israel J. Math., 227 (2018), 843--859.
- Existence of regular unimodular triangulations of dilated empty simplices (with T. Hibi and K. Yoshida),
European J. Combin., 70 (2018), 374--383.
- 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.
- Lattice multipolygons (with M. Masuda),
Kyoto J. Math., 57 (2017), 807--828.
- Interlacing Ehrhart Polynomials of Reflexive Polytopes (with M. Kummer and M. Michalek),
Selecta Math., 23 (2017), 2977--2998.
- Integer decomposition property of free sums of convex polytopes (with T. Hibi),
Ann. Comb., 20 (2016), 601--607.
- Minkowski sum of polytopes and its normality,
J. Math. Soc. Japan., 68 (2016), 1147--1159.
- Almost Gorenstein homogeneous rings and their h-vectors,
J. Alg., 456 (2016), 190--206.
- 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.
- Smooth Fano polytopes arising from finite directed graphs,
Kyoto J. Math., 55 (2015), 579--592.
- Algebraic study on Cameron-Walker graphs (with T. Hibi, K. Kimura and A. B. O'Keefe),
J. Alg., 422 (2015), 257--269.
- Toric rings arising from cyclic polytopes (with T. Hibi, L. Katthän and R. Okazaki),
Comm. Algebra, 43 (2015), 778--794.
- Non-normal very ample polytopes and their holes,
Electron. J. Combin., 21 (2014), 1--12.
- Ehrhart polynomials of integral simplices with prime volumes,
INTEGERS, 14 (2014), 1--15.
- Integer decomposition property of dilated polytopes (with D. A. Cox, C. Haase and T. Hibi),
Electron. J. Combin., 21 (2014), 1--17.
- Depth of initial ideals of normal edge rings (with T. Hibi, K. Kimura and A. B. O'Keefe),
Comm. Algebra, 42 (2014), 2908--2922.
- 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.
- Hermite normal forms and δ-vector (with T. Hibi and N. Li),
J. Comb. Theory Ser. A 119 (2012), 1158--1173.
- Counterexamples of the conjecture on roots of Ehrhart polynomials,
Discrete Comput. Geom. 47 (2012), 618--623.
- Roots of Ehrhart polynomials arising from graphs (with T. Matsui, Y. Nagazawa, H. Ohsugi and T. Hibi),
J. Algebr. Comb. 34 (2011), 721--749.
- 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.
- Roots of Ehrhart polynomials of Gorenstein Fano polytopes (with T. Hibi and H. Ohsugi),
Proc. Amer. Math. Soc. 139 (2011), 3727--3734.
- Smooth Fano polytopes arising from finite partially ordered sets (with T. Hibi),
Discrete Comput. Geom. 45 (2011), 449--461.
- Ehrhart polynomials of convex polytopes with small volumes (with T. Hibi and Y. Nagazawa),
European J. Combin. 32 (2011), 226--232.
- Shifted symmetric δ-vectors of convex polytopes,
Discrete Math. 310 (2010), 2925--2934.
Preprints (submitted)
- Combinatorics of graded module categories over skew polynomial algebras at roots of unity (with K. Ueyama)
- Classification of generalized Alexander quandles (with S. Kamada, J. Kosaka and H. Kurihara)
- Characteristic quasi-polynomials of deletions of Shi arrangements of type B and their period collapse (with N. Nakashima)
- Non-finitely generated monoids corresponding to finitely generated homogeneous subalgebras (with K. Tani)
- On the Ehrhart Theory of Generalized Symmetric Edge Polytopes (with R. Davis and H. Ohsugi)
- Ehrhart quasi-polynomials and parallel translations (with S. Murai and M. Yoshinaga)
- Fans and polytopes in tilting theory II: g-fans of rank 2 (with T. Aoki, O. Iyama, R. Kase and Y. Mizuno)
- Restricted Chain-Order Polytopes via Combinatorial Mutations (with O. Clarke and F. Zaffalon)
- Fans and polytopes in tilting theory I: Foundations (with T. Aoki, O. Iyama, R. Kase and Y. Mizuno)
- Two poset polytopes are mutation-equivalent
Publications (Japanese)
- 『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
- 『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