The Optimal Lower Bound for Generators of Invariant Rings without Finite SAGBI Bases with Respect to Any Admissible Order

Abstract : We prove the existence of an invariant ring \textbfC[X_1,...,X_n]^T generated by elements with a total degree of at most 2, which has no finite SAGBI basis with respect to any admissible order. Therefore, 2 is the optimal lower bound for the total degree of generators of invariant rings with such a property.
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Discrete Mathematics and Theoretical Computer Science, DMTCS, 1999, 3 (2), pp.65-70
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Manfred Göbel. The Optimal Lower Bound for Generators of Invariant Rings without Finite SAGBI Bases with Respect to Any Admissible Order. Discrete Mathematics and Theoretical Computer Science, DMTCS, 1999, 3 (2), pp.65-70. 〈hal-00958927〉

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