Rings of polynomial invariants of the alternating group have no finite SAGBI bases with respect to any admissible order
It is well known, that the invariant ring C[X-1, X-2, X-3](A3) of the alternating group A(3) is the "smallest" ring of polynomial invariants of a permutation group with respect to the number of variables and the number of generators, which has no finite SAGBI basis with respect to any admissible order. We show in this note that for any number of variables n greater than or equal to 3 the invariant ring C[X-1,..., X-n](An) has no finite SAGBI basis with respect to any admissible order. (C) 2000 Elsevier Science B.V. All rights reserved.
alternating groups sagbi bases admissible orders algorithmic invariant theory