Current Trends on Gröbner Bases: The 50th Anniversary of Gröbner Bases
July 1–10, 2015 | Osaka, Japan
The 50th Anniversary of Gröbner Bases

Editor(s) Takayuki Hibi

Adv. Stud. Pure Math., 77: 436pp. (2018). DOI: 10.2969/aspm/07710000
TABLE OF CONTENTS
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Advanced Studies in Pure Mathematics Vol. 77, - (2018).
Bruno Buchberger
Advanced Studies in Pure Mathematics Vol. 77, - (2018).
Takayuki Hibi
Advanced Studies in Pure Mathematics Vol. 77, - (2018).
Advanced Studies in Pure Mathematics Vol. 77, - (2018).
John Abbott , Anna Maria Bigatti
Advanced Studies in Pure Mathematics Vol. 77, 1-24 (2018). https://doi.org/10.2969/aspm/07710001
KEYWORDS: Gröbner bases, elimination, term orderings, modular methods, software library, 13-04, 13P10, 68W30, 13P15, 14Q10, 05E40, 68W25
Bruno Buchberger
Advanced Studies in Pure Mathematics Vol. 77, 25-33 (2018). https://doi.org/10.2969/aspm/07710025
KEYWORDS: Gröbner basis, $S$-polynomial, Macaulay matrix, 33F10, 13P10
Mathias Drton
Advanced Studies in Pure Mathematics Vol. 77, 35-86 (2018). https://doi.org/10.2969/aspm/07710035
KEYWORDS: algebraic statistics, covariance matrix, Gaussian distribution, graphical model, Gröbner basis, structural equation model, 62H05, 13P25, 05C90
Claudia Fassino , Hans Michael Möller , Eva Riccomagno
Advanced Studies in Pure Mathematics Vol. 77, 87-107 (2018). https://doi.org/10.2969/aspm/07710087
KEYWORDS: least squares estimates, vanishing ideals, Gröbner bases, 13P, 62J, 65F, 13P10, 65F20
Elizabeth Gross , Sonja Petrović , Donald Richards , Despina Stasi
Advanced Studies in Pure Mathematics Vol. 77, 109-119 (2018). https://doi.org/10.2969/aspm/07710109
KEYWORDS: maximum likelihood estimation, factor analysis, multiple roots, inference, small sample, 62F10, 62N02, 62H25, 62H12, 62H20, 62F30
Akihiro Higashitani , Kyouko Kimura
Advanced Studies in Pure Mathematics Vol. 77, 121-128 (2018). https://doi.org/10.2969/aspm/07710121
KEYWORDS: Serre's condition $(S_2)$, edge ring, toric ideal, finite graph, 13H10
Christopher J. Hillar , Robert Krone , Anton Leykin
Advanced Studies in Pure Mathematics Vol. 77, 129-154 (2018). https://doi.org/10.2969/aspm/07710129
KEYWORDS: Invariant ideal, well-quasi-ordering, symmetric group, Gröbner basis, generating sets, infinite dimensional algebra, 13E05, 13E15, 20B30, 06A07
Florian Kohl , Yanxi Li , Johannes Rauh , Ruriko Yoshida
Advanced Studies in Pure Mathematics Vol. 77, 155-170 (2018). https://doi.org/10.2969/aspm/07710155
KEYWORDS: feasibility problem, lattice points, polytopes, software, 11P21, 52B11, 90C08, 97K70
Nicolette Meshkat , Zvi Rosen , Seth Sullivant
Advanced Studies in Pure Mathematics Vol. 77, 171-205 (2018). https://doi.org/10.2969/aspm/07710171
KEYWORDS: identifiability, observability, indistinguishability, state space models, 13P10, 13P25, 05E40, 52B20
Mateusz Michałek
Advanced Studies in Pure Mathematics Vol. 77, 207-252 (2018). https://doi.org/10.2969/aspm/07710207
KEYWORDS: toric variety, algebraic combinatorics, matroid, cut polytope, algebraic phylogenetics, 14M25
Toshinori Oaku
Advanced Studies in Pure Mathematics Vol. 77, 253-352 (2018). https://doi.org/10.2969/aspm/07710253
KEYWORDS: $D$-module, Gröbner basis, generalized function, probability density function, 13N10, 13P10, 46F10, 62E15
Toshinori Oaku
Advanced Studies in Pure Mathematics Vol. 77, 353-398 (2018). https://doi.org/10.2969/aspm/07710353
KEYWORDS: $D$-module, Gröbner basis, localization, local cohomology, $b$-function, hyperplane arrangement, multiplicity, 14F10, 13P10, 13D45, 14B15, 52C35
Tran Nam Trung
Advanced Studies in Pure Mathematics Vol. 77, 399-409 (2018). https://doi.org/10.2969/aspm/07710399
KEYWORDS: planar graph, edge ideal, Gorenstein ring, 13D45, 05C90, 05E40, 05E45
Raimundas Vidunas , Akimichi Takemura
Advanced Studies in Pure Mathematics Vol. 77, 411-436 (2018). https://doi.org/10.2969/aspm/07710411
KEYWORDS: complex Wishart distribution, holonomic systems, 60E05, 13N10, 62H10
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