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Stanley decompositions of the bracket ring. (English) Zbl 0727.13005
We give an explicit Stanley decomposition of the bracket ring ${\bbfB}\sb{n,d}$, that is, the commutative ring generated by the $d\times d$-minors of a generic $n\times d$-matrix. A Stanley decomposition is a direct sum decomposition of the additive group of the ring, each summand of which is a bracket monomial times a subring generated freely by brackets. The decomposition is obtained via a shelling of the simplicial complex determined by the standard tableaux. Our construction has important applications in the Cushman-Sanders normal form theory for nilpotent vector fields.
Reviewer: N.White (Gainesville)

13C40Linkage, complete intersections and determinantal ideals
13F20Polynomial rings and ideals
14M12Determinantal varieties
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