Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- The 50th Anniversary of Gröbner Bases, T. Hibi, ed. (Tokyo: Mathematical Society of Japan, 2018), 129 - 154
Equivariant Gröbner bases
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.
Received: 5 October 2016
Revised: 31 March 2017
First available in Project Euclid: 21 September 2018
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Digital Object Identifier
Primary: 13E05: Noetherian rings and modules 13E15: Rings and modules of finite generation or presentation; number of generators 20B30: Symmetric groups 06A07: Combinatorics of partially ordered sets
Hillar, Christopher J.; Krone, Robert; Leykin, Anton. Equivariant Gröbner bases. The 50th Anniversary of Gröbner Bases, 129--154, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07710129. https://projecteuclid.org/euclid.aspm/1537499601