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List of Papers
Toshio Sumi Last modified date：2024.01.15

Professor / Division for Theoretical Natural Science / Faculty of Arts and Science


Papers
1. Taizo Kanenobu, Toshio Sumi, Extension of Takahashi’s ribbon 2knots with isomorphic groups, Journal of Knot Theory and Its Ramifications, 10.1142/S021821652350013X, 32, 2, 2350013 (12 pages), 2023.03, We give infinitely many pairs of ribbon 2-knots of 1-fusion in S4 with isomorphic knot groups, which extend Takahashi’s examples. They are distinguished by the trace sets, which are calculated by using SL(2, C)-representations of the knot groups..
2. Taizo Kanenobu, Toshio Sumi, Twisted Alexander polynomial of a ribbon 2-knot of 1-fusion, Osaka Journal of Mathematics, 57, 4, 789-803, 2020.10.
3. Taizo Kanenobu, Toshio Sumi, Suciu's ribbon 2-knots with isomorphic group, Journal of Knot Theory and Its Ramifications, https://doi.org/10.1142/S0218216520500534, 29, 7, 2050053 (9 pages), 2020.09.
4. Taizo Kanenobu, Toshio Sumi, Classification of ribbon 2-knots presented by virtual arcs with up to four crossings, Journal of Knot Theory and Its Ramifications, http://dx.doi.org/10.1142/S0218216519500676, 28, 10, 1950067 (18 pages), 2019.10.
5. Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata, Typical ranks of semi-tall real 3-tensors, Linear and Multilinear Algebra, 10.1080/03081087.2019.1637811, 2019.07.
6. Taizo Kanenobu, Toshio Sumi, Classification of a family of ribbon 2-knots with trivial Alexander polynomial, Communications of the Korean Mathematical Society, http://doi.org/10.4134/CKMS.c170222, 33, 2, 591-604, 2018.04.
7. Mitsuhiro Miyazaki, Toshio Sumi, Toshio Sakata, Typical ranks of certain 3-tensors and absolutely full column rank tensors, Linear and Multilinear Algebra, http://www.tandfonline.com/doi/abs/10.1080/03081087.2017.1292994, 66, 1, 193-205, 2017.03, In this paper, we study typical ranks of 3-tensors and show that there are plural typical ranks for m x n x p tensors over the real number field in the following cases: (1) 3≦m≦h(n) and (m-1)(n-1)+1≦p≦(m-1)n, where h is the Hurwitz-Radon function, (2) m=3, n=3 (mod 4) and p=2n-1, (3) m=4, n=2 (mod 4), n≧6 and p=3n-2, (4) m=6, n=4 (mod 8), n≧12 and p=5n-4, (5) m=10, n=24 (mod 32) and p=9n-8..
8. Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata, Typical ranks for 3-tensors, nonsingular bilinear maps and determinantal ideals, Journal of Algebra, http://dx.doi.org/10.1016/j.jalgebra.2016.09.028, 471, 1, 409-453, 2017.02, Let m,n≥3, (m−1)(n−1)+2≤p≤mn, and u=mn−p. The set Ru×n×m of all real tensors with size u×n×m is one to one corresponding to the set of bilinear maps Rm×Rn→Ru. We show that Rm×n×p has plural typical ranks p and p+1 if and only if there exists a nonsingular bilinear map Rm×Rn→Ru. We show that there is a dense open subset O of Ru×n×m such that for any Y∈O, the ideal of maximal minors of a matrix defined by Y in a certain way is a prime ideal and the real radical of that is the irrelevant maximal ideal if that is not a real prime ideal. Further, we show that there is a dense open subset T of Rn×p×m and continuous surjective open maps ν:O→Ru×p and σ:T→Ru×p, where Ru×p is the set of u×p matrices with entries in R, such that if ν(Y)=σ(T), then rank T=p if and only if the ideal of maximal minors of the matrix defined by Y is a real prime ideal..
9. Toshio Sumi, Richness of Smith equivalent modules for finite gap Oliver groups, Tohoku Journal of Mathematics, doi:10.2748/tmj/1474652268, 68, 3, 457-469, 2016.09, [URL].
10. Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata, Typical rank of mxnx(m-1)n tensors with 3Linear and Multilinear Algebra, http://dx.doi.org/10.1080/03081087.2014.910206, 63, 5, 940-955, 2015.07, Let 3\rho(n), then the set of m x n x (m-1)n tensors has only one typical rank (m-1)n..
11. Toshio Sumi, Toshio Sakata, Mitsuhiro Miyazaki, Rank of tensors with size 2 x ... x 2, Far East J. Math. Sci., 90, 2, 141-162, 2014.08, We study an upper bound of ranks of n-tensors with size 2×⋯×2 over the complex and real number field. We characterize a 2×2×2 tensor with rank 3 by using the Cayley's hyperdeterminant and some function. Then we see another proof of Brylinski's result that the maximal rank of 2×2×2×2 complex tensors is 4. We state supporting evidence of the claim that 5 is a typical rank of 2×2×2×2 real tensors. Recall that Kong and Jiang show that the maximal rank of 2×2×2×2 real tensors is less than or equal to 5. The maximal rank of 2×2×2×2 complex (resp. real) tensors gives an upper bound of the maximal rank of 2×⋯×2 complex (resp. real) tensors..
12. Toshio Sumi, Centralizers of gap groups, Fundamenta Mathematicae, 10.4064/fm226-2-1, 226, 101-121, 2014.06, A finite group G is called a gap group if there exists an RG-module which has no large isotropy groups except at zero and satisfies the gap condition. The gap condition facilitates the process of equivariant surgery. Many groups are gap groups and also many groups are not. In this paper, we clarify the relation between a gap group and the structures of its centralizers. We show that a nonsolvable group which has a normal, odd prime power index proper subgroup is a gap group..
13. 角 俊雄, Smith sets of non-solvable groups whose nilquotients are cyclic groups of order 1,2, or 3, RIMS Kokyuroku Bessatsu, B39, 149-165, 2013.06, Let $G$ be a finite group.
Two real $G$-modules $U$ and $V$ are called Smith equivalent
if there exists a smooth action of $G$
on a sphere with two fixed points at which tangential representations are isomorphic to $U$ and $V$ respectively. The Smith set of $G$ is the subset of the real representation ring of $G$ consisting differences of Smith equivalent $G$-modules. We discuss when the Smith set of an Oliver group becomes an abelian group and give several examples of non-solvable groups of which the Smith sets are groups.
.
14. Krzysztof Pawalowski, Toshio Sumi, The Laitinen Conjecture for finite non-solvable groups, Proceedings of the Edinburgh Mathematical Society , http://dx.doi.org/10.1017/S0013091512000223, 56, 1, 303-336, 2013.02, For any finite group G, we impose an algebraic condition, the G^{nil}-coset condition, and prove that any finite Oliver group G satisfying the G^{nil}-coset condition has a smooth action on some sphere with isolated fixed points at which the tangent G-modules are not isomorphic to each other. Moreover, we prove that, for any finite non-solvable group G not isomorphic to Aut(A_{6}) or PΣL(2, 27), the G\sup{nil}-coset condition holds if and only if r_{G} ≥ 2, where r_{G} is the number of real conjugacy classes of elements of G not of prime power order. As a conclusion, the Laitinen Conjecture holds for any finite non-solvable group not isomorphic to Aut(A_{6})..
15. Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata, Typical ranks for m x n x (m-1)n tensors with mLinear Algebra and its Applications, 10.1016/j.laa.2011.08.009, 438, 2, 953-958, 2013.01, In various application fields, tensor type data are used recently and
then a typical rank is important. There may be more than one typical
ranks over the real number field. It is well known that the set of
2 × n × n tensors has two typical ranks n, n + 1 for n>=2, that the
set of 3 × 4 × 8 tensors has two typical ranks 8, 9, and that the set
of 4×4×12 tensors has two typical ranks 12, 13. In this paper, we
show that the set of m×n×(m−1)n tensors with mtypical ranks (m − 1)n, (m − 1)n + 1 if mHurwitz–Radon function..
16. Toshio Sakata, Kazumitsu Maehara, Takeshi Sasaki, Toshio Sumi, Mitsuhiro Miyazaki, Yoshitaka Watanabe, and Makoto Tagami , Tests of inequivalence among absolutely nonsingular tensors through geometric invariants, Universal Journal of Mathematics and Mathematical Sciences , 1, 1, 1-28, 2012.02, [URL].
17. Toshio Sumi, The gap hypothesis for finite groups which have an abelian quotient group not of order a power of 2, Journal of the Mathematical Society of Japan, 10.2969/jmsj/06410091, 64, 1, 91-106, 2012.01.
18. Toshio Sumi and Toshio Sakata, Connectivity for 3x3xK contingency tables, Journal of Algebraic Statistics, 2, 1, 54-74, 2011.08, [URL].
19. Toshio Sumi and Toshio Sakata, 2-neighborhood theorem for 3x3x3 contingency tables, Journal of the Indian Society for Probability and Statistics, 12, 66-84, 2010.12.
20. Toshio Sumi, Representation spaces fulfilling the gap hypothesis, Proceedings of the International Conference Bratislava Topology Symposium "Group Actions and Homogeneous Spaces", 99-116, 2010.10.
21. Toshio Sumi and Toshio Sakata, The Set of 3x4x4 Contingency Tables has 3-Neighborhood Property, Proceedings of COMPSTAT'2010, Electronic Supplementary Material (e-book) 19th International Conference on Computational Statistics, Paris France, August 22-27, 2010, 1629-1636, 2010.09.
22. Toshio Sumi, Mitsuhiro Miyazaki, and Toshio Sakata, About the maximal rank of 3-tensors over the real and the complex number field, Ann. Inst. Stat. Math., 10.1007/s10463-010-0294-5, 62, 807-822, 2010.09.
23. Toshio Sumi, Mitsuhiro Miyazaki, and Toshio Sakata, Rank of 3-tensors with 2 slices and Kronecker canonical forms, Linear Algebra and its Applications, vol. 431, 1858-1868, 2009.10.
24. Mitsuhiro Miyazaki, Toshio Sumi and Toshio Sakata, Tensor rank determination problem, Nonlinear Theory and its Applications, 2009.10.
25. Krzysztof Pawalowski and Toshio Sumi, The Laitinen Conjecture for finite solvable Oliver groups, Proceedings of American Mathematical Society, Proceedings of the American Mathematical Society 137 (6), 2147-2156, 2009, 2009.06.
26. Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki, The Evaluation of the Maximal Rank of Tensors Simply by Row and Column Operations and Symmetrization, Joint Meeting of 4th World Conference of the IASC and 6th Conference of the Asian Regional Section of the IASC on Computational Statistics & Data Analysis, 2008.12.
27. Toshio Sakata and Toshio Sumi, Lifting Between the Sets of Three-Way Contingency Tables and R-Neighbourhood Property
, International Conference on Computational Statistics, Proceedings in Computational Statistics 18th Symposium Held in Porto, Portugal, 2008, 2008.08.
28. T. Sumi and T. Sakata, A Sufficient Condition for the Unique Solution of Non-Negative Tensor Factorization, Independent Component Analysis and Signal Separation, 7th International Conference, ICA 2007, Lecture Notes in Computer Science, M.E.Davies, C.J.James, S.A.Abdallah and M.D.Plumbley (Eds.) , pp. 113-120, 2007.09.
29. T. Sumi, GAP MODULES FOR SEMIDIRECT PRODUCT GROUPS, Kyushu Journal of Mathematics, Vol. 58 No. 1, pp. 33-58, 2004.03.
30. T. Sumi, Gap modules for direct product groups, Jour. Math. Soc. Japan, Vol. 53, No. 4, pp. 975--990, 2001.10.
31. M.　Morimoto, T. Sumi and M. Yanagihara, Finite groups possessing gap modules, Contemp. Math., Vol.~258, pp.~329--342, 2000.01.
32. N. Iwase, T. Sumi and S. Saito, Homology of the universal covering of a co-H-space, Trans. Amer. Math. Soc., 10.1090/S0002-9947-99-02238-2, 351, 12, 4837-4846, Vol. 351, No. 12, pp. 4837-4846, 1999.01.


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