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VOL. 77 | 2018 Equivariant Gröbner bases
Christopher J. Hillar, Robert Krone, Anton Leykin

Editor(s) Takayuki Hibi

Adv. Stud. Pure Math., 2018: 129-154 (2018) DOI: 10.2969/aspm/07710129


Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables until recently when theoretical efforts have made possible the development of effective routines. Ability to compute relies on finite generation up to symmetry for ideals invariant under a large group or monoid action, such as the permutations of the natural numbers. We summarize the current state of theory and applications for equivariant Gröbner bases, develop several algorithms to compute them, showcase our software implementation, and close with several open problems and computational challenges.


Published: 1 January 2018
First available in Project Euclid: 21 September 2018

zbMATH: 07034252
MathSciNet: MR3839709

Digital Object Identifier: 10.2969/aspm/07710129

Primary: 06A07 , 13E05 , 13E15 , 20B30

Keywords: generating sets , Gröbner basis , infinite dimensional algebra , invariant ideal , Symmetric group , well-quasi-ordering

Rights: Copyright © 2018 Mathematical Society of Japan


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