-
Projective dimensions of hyperplane arrangements
Peer-reviewed
Takuro Abe
Transactions of the American Mathematical Society377
(
11
)
7793
-
7827
11 2024
-
Free reflection multiarrangements and quasi-invariants
Peer-reviewed
International coauthorship
Takuro Abe, Naoya Enomoto, Misha Feigin, Masahiko Yoshinaga
International Mathematics Research Notices
22 10 2024
-
Projective dimension of weakly chordal graphic arrangements
Peer-reviewed
International coauthorship
Takuro Abe, Lukas Kühne, Paul Muecksch, Leonie Muehlherr
Algebraic Combinatorics, accepted
10 2024
-
A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups
Peer-reviewed
Takuro Abe, Gerhard Roehrle, Christian Stump, Masahiko Yoshinaga
Journal of Combinatorial Algebra8
(
3/4
)
251
-
278
23 7 2024
-
Vertex-weighted digraphs and freeness of arrangements between Shi and Ish
Peer-reviewed
Takuro Abe, Tan Nhat Tran, Shuhei Tsujie
European Journal of Combinatorics118
5 2024
-
Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one
Peer-reviewed
ABE, TAKURO
Algebraic Combinatorics7
(
2
)
413
-
429
29 4 2024
-
On some freeness-type properties for line arrangements
Peer-reviewed
Takuro Abe, Denis Ibadula, Anca Măcinic
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE25
(
1
)
427
-
447
2 2024
-
Addition-deletion theorems for the Solomon-Terao polynomials and B-sequences of hyperplane arrangements
Peer-reviewed
International journal
Abe, Takuro
Mathematische Zeitschrift306
(
205
)
11 1 2024
-
Addition-deletion theorem for free hyperplane arrangements and combinatorics
Peer-reviewed
Takuro Abe
Journal of Algebra610
1
-
17
19 7 2022
-
Double points of free projective line arrangements
Peer-reviewed
Takuro Abe
International Mathematical Research Notices2022
(
3
)
1811
-
1824
2 2022
-
Locally heavy hyperplanes in multiarrangements
Peer-reviewed
Takuro Abe, Lukas Kühne
Journal of Pure and Applied Algebra226
(
1
)
106791
-
106791
1 2022
-
Roots of the characteristic polynomials of hyperplane arrangements and their restrictions and localizations
Peer-reviewed
Takuro Abe
Topology and its Applications (special volume), to appear
12 2021
-
A Hyper-surface Arrangement Model of Ranking Distributions
Peer-reviewed
Shizuo Kaji, Akira Horiguchi, Takuro Abe, Yohsuke Watanabe
Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining
796
-
804
14 8 2021
-
A Characterization of High Order Freeness for Product Arrangements and Answers to Holm’s Questions
Peer-reviewed
International journal
Takuro Abe, Norihiro Nakashima
Algebras and Representation Theory24
(
3
)
585
-
599
6 2021
-
Plus-one generated and next to free arrangements of hyperplanes
Peer-reviewed
Takuro Abe
International Mathematical Research Notices2021
(
12
)
9233
-
9261
6 2021
-
Addition–deletion results for the minimal degree of logarithmic derivations of hyperplane arrangements and maximal Tjurina line arrangements
Takuro Abe, Alexandru Dimca, Gabriel Sticlaru
Journal of Algebraic Combinatorics
16 11 2020
-
On A_1^2 restrictions of Weyl arrangements
Peer-reviewed
Takuro Abe, Hiroaki Terao, Tan Nhat Tran
Journal of Algebraic Combinatorics
18 9 2020
-
Hessenberg varieties and hyperplane arrangements
Peer-reviewed
Takuro Abe, Tatsuya Horiguchi, Mikiya Masuda, Satoshi Murai, Takashi Sato
Journal für die reine und angewandte Mathematik (Crelles Journal)2020
(
764
)
241
-
286
1 7 2020
-
On complex supersolvable line arrangements
Peer-reviewed
Takuro Abe, Alexandru Dimca
Journal of Algebra552
38
-
51
6 2020
-
Multiple addition, deletion and restriction theorems for hyperplane arrangements
Peer-reviewed
Takuro Abe, Hiroaki Terao
Proceedings of the American Mathematical Society147
(
11
)
4835
-
4845
11 2019
-
Solomon-Terao algebra of hyperplane arrangements
Peer-reviewed
Abe, Takuro, Maeno, Toshiaki, Mural, Satoshi, Numata, Yasuhide
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN71
(
4
)
1027
-
1047
10 2019
-
Deletion theorem and combinatorics of hyperplane arrangements
Peer-reviewed
Takuro Abe
Mathematische Annalen373
(
1--2
)
581
-
595
2 2019
-
Heavy hyperplanes in multiarrangements and their freeness
Peer-reviewed
Takuro Abe, Lukas Kuehne
Journal of Algebraic Combinatorics48
(
4
)
581
-
606
12 2018
-
Splitting types of bundles of logarithmic vector fields along plane curves
Peer-reviewed
Takuro Abe, Alexandru Dimca
International Journal of Mathematics29
(
8
)
2018
-
A basis construction of the extended Catalan and Shi arrangements of the type &ITA&IT2
Peer-reviewed
Takuro Abe, Daisuke Suyama
JOURNAL OF ALGEBRA493
20
-
35
1 2018
-
The freeness of Ish arrangements
Peer-reviewed
Takuro Abe, Daisuke Suyama, Shuhei Tsujie
JOURNAL OF COMBINATORIAL THEORY SERIES A146
169
-
183
2 2017
-
Restrictions of free arrangements and the division theorem
Peer-reviewed
Takuro Abe
Springer INdAM Series19
389
-
401
2017
-
Non-recursive freeness and non-rigidity
Peer-reviewed
T. Abe, M. Cuntz, H. Kawanoue, T. Nozawa
DISCRETE MATHEMATICS339
(
5
)
1430
-
1449
5 2016
-
Divisionally free arrangements of hyperplanes
Peer-reviewed
Takuro Abe
INVENTIONES MATHEMATICAE204
(
1
)
317
-
346
4 2016
-
Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements
Peer-reviewed
Takuro Abe, Hiroaki Terao
JOURNAL OF ALGEBRAIC COMBINATORICS43
(
1
)
33
-
44
2 2016
-
The freeness of ideal subarrangements of Weyl arrangements
Peer-reviewed
T. Abe, M. Barakat, M. Cuntz, T. Hoge, H. Terao
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY18
(
6
)
1339
-
1348
2016
-
LOGARITHMIC BUNDLES OF DEFORMED WEYL ARRANGEMENTS OF TYPE A(2)
Peer-reviewed
Takuro Abe, Daniele Faenzi, Jean Valles
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE144
(
4
)
745
-
761
2016
-
A mathematical problem for security analysis of hash functions and pseudorandom generators
Peer-reviewed
Koji Nuida, Takuro Abe, Shizuo Kaji, Toshiaki Maeno, Yasuhide Numata
International Journal of Foundations of Computer Science26
(
2
)
169
-
194
8 2 2015
-
Simple-root bases for Shi arrangements
Peer-reviewed
Takuro Abe, Hiroaki Terao
JOURNAL OF ALGEBRA422
89
-
104
1 2015
-
Roots of characteristic polynomials and intersection points of line arrangements.
Peer-reviewed
Takuro Abe
Journal of Singularities8
100
-
117
10 2014
-
Free arrangements and coefficients of characteristic polynomials
Peer-reviewed
Takuro Abe, Masahiko Yoshinaga
Mathematische Zeitschrift275
(
3-4
)
911
-
919
12 2013
-
Chambers of 2-affine arrangements and freeness of 3-arrangements
Peer-reviewed
Takuro Abe
JOURNAL OF ALGEBRAIC COMBINATORICS38
(
1
)
65
-
78
8 2013
-
Characteristic Polynomials, eta-Complexes, and Freeness of Tame Arrangements
Peer-reviewed
Takuro Abe
MICHIGAN MATHEMATICAL JOURNAL62
(
1
)
117
-
130
2013
-
Equivariant multiplicities of Coxeter arrangements and invariant bases
Peer-reviewed
Takuro Abe, Hiroaki Terao, Atsushi Wakamiko
ADVANCES IN MATHEMATICS230
(
4-6
)
2364
-
2377
7 2012
-
Exponents of 2-multiarrangements and multiplicity lattices
Peer-reviewed
Takuro Abe, Yasuhide Numata
JOURNAL OF ALGEBRAIC COMBINATORICS35
(
1
)
1
-
17
2 2012
-
ON A CONJECTURE OF ATHANASIADIS RELATED TO FREENESS OF A FAMILY OF HYPERPLANE ARRANGEMENTS
Peer-reviewed
Takuro Abe
MATHEMATICAL RESEARCH LETTERS19
(
2
)
469
-
474
2012
-
The freeness of Shi-Catalan arrangements
Peer-reviewed
Takuro Abe, Hiroaki Terao
EUROPEAN JOURNAL OF COMBINATORICS32
(
8
)
1191
-
1198
11 2011
-
Primitive filtrations of the modules of invariant logarithmic forms of Coxeter arrangements
Peer-reviewed
Takuro Abe, Hiroaki Terao
JOURNAL OF ALGEBRA330
(
1
)
251
-
262
3 2011
-
A primitive derivation and logarithmic differential forms of Coxeter arrangements
Peer-reviewed
Takuro Abe, Hiroaki Terao
MATHEMATISCHE ZEITSCHRIFT264
(
4
)
813
-
828
4 2010
-
Coxeter multiarrangements with quasi-constant multiplicities
Peer-reviewed
Takuro Abe, Masahiko Yoshinaga
JOURNAL OF ALGEBRA322
(
8
)
2839
-
2847
10 2009
-
Signed-eliminable graphs and free multiplicities on the braid arrangement
Peer-reviewed
Takuro Abe, Koji Nuida, Yasuhide Numata
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES80
121
-
134
8 2009
-
The Stability of the Family of B2-Type Arrangements
Peer-reviewed
Takuro Abe
COMMUNICATIONS IN ALGEBRA37
(
4
)
1193
-
1215
2009
-
TOTALLY FREE ARRANGEMENTS OF HYPERPLANES
Peer-reviewed
Takuro Abe, Hiroaki Terao, Masahiko Yoshinaga
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY137
(
4
)
1405
-
1410
2009
-
The Euler multiplicity and addition-deletion theorems for multiarrangements
Peer-reviewed
Takuro Abe, Hiroaki Terao, Max Wakefield
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES77
335
-
348
4 2008
-
Splitting criterion for reflexive sheaves
Peer-reviewed
Takuro Abe, Masahiko Yoshinaga
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY136
(
6
)
1887
-
1891
2008
-
The characteristic polynomial of a multiarrangement
Peer-reviewed
Takuro Abe, Hiroaki Terao, Max Wakefield
ADVANCES IN MATHEMATICS215
(
2
)
825
-
838
11 2007
-
Free and non-free multiplicity on the deleted A(3) arrangement
Peer-reviewed
Takuro Abe
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES83
(
7
)
99
-
103
10 2007
-
The elementary transformation of vector bundles on regular schemes
Peer-reviewed
Takuro Abe
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY359
(
9
)
4285
-
4295
2007
-
The stability of the family of A<sub>2</sub>-type arrangements
Peer-reviewed
T. Abe
Journal of Mathematics of Kyoto University46
(
3
)
617
-
636
2006