Let K be a field; let ~mK" be a finite set and let 3(N)mK[xl ..... x,] be the ideal of ~. A purel... more Let K be a field; let ~mK" be a finite set and let 3(N)mK[xl ..... x,] be the ideal of ~. A purely combinatorial algorithm to obtain a linear basis of the quotient algebra K Ix1 ..... x,]/3(~) is given. Such a basis is represented by an n-dimensional Ferrers diagram of monomials which is minimal with respect to the inverse lexicographical order ~<i.l.-It is also shown how this algorithm can be extended to the case in which ~ is an algebraic multiset. A few applications are stated (among them, how to determine a reduced Grfbner basis of 3(,~) with respect to %i.1. without using Buchberger's algorithm).
New algorithms to perform both the generalizations due to Knuth [2] of the Robinson-Schensted cor... more New algorithms to perform both the generalizations due to Knuth [2] of the Robinson-Schensted correspondence and their inverse correspondences are given. 1. Preliminary definitions Let EE(O, l}; throughout this paper we shall consider two-line arrays such as b, bz ... b, CT= ((bi, ai)EN X N) a, a, '+. a, wherebiGbi.1 andbi=bi+l *ai < ai+ I + E. We use the term E-two-line array for such * Corresponding author.
The K-linear space of all n-linearly recursive functions (1.1) =evaluated differential forms) for... more The K-linear space of all n-linearly recursive functions (1.1) =evaluated differential forms) for which a zero-dimensional ideal ⊂ K x 1 x n is the largest ideal which is contained in the kernel of all of them turns out to be the orthogonal K-space ⊥ ⊂ K x 1 x n * of and is known as Macaulay's inverse system of. Making use of the antiderivative operator , the whole space of all differential forms can be endowed with a structure of K x 1 x n-module; with respect to finitely generated submodules of it (which we call Macaulay modules), we describe a dual analog of the Gröbner bases theory. The motivation for studying Macaulay modules has to be found mainly in multivariate interpolation problems and in the theory of polynomial bialgebras, though some application to algebraic geometry is not excluded.
Let K be a field; let ~mK" be a finite set and let 3(N)mK[xl ..... x,] be the ideal of ~. A purel... more Let K be a field; let ~mK" be a finite set and let 3(N)mK[xl ..... x,] be the ideal of ~. A purely combinatorial algorithm to obtain a linear basis of the quotient algebra K Ix1 ..... x,]/3(~) is given. Such a basis is represented by an n-dimensional Ferrers diagram of monomials which is minimal with respect to the inverse lexicographical order ~<i.l.-It is also shown how this algorithm can be extended to the case in which ~ is an algebraic multiset. A few applications are stated (among them, how to determine a reduced Grfbner basis of 3(,~) with respect to %i.1. without using Buchberger's algorithm).
New algorithms to perform both the generalizations due to Knuth [2] of the Robinson-Schensted cor... more New algorithms to perform both the generalizations due to Knuth [2] of the Robinson-Schensted correspondence and their inverse correspondences are given. 1. Preliminary definitions Let EE(O, l}; throughout this paper we shall consider two-line arrays such as b, bz ... b, CT= ((bi, ai)EN X N) a, a, '+. a, wherebiGbi.1 andbi=bi+l *ai < ai+ I + E. We use the term E-two-line array for such * Corresponding author.
Let K be a field; let ~mK" be a finite set and let 3(N)mK[xl ..... x,] be the ideal of ~. A purel... more Let K be a field; let ~mK" be a finite set and let 3(N)mK[xl ..... x,] be the ideal of ~. A purely combinatorial algorithm to obtain a linear basis of the quotient algebra K Ix1 ..... x,]/3(~) is given. Such a basis is represented by an n-dimensional Ferrers diagram of monomials which is minimal with respect to the inverse lexicographical order ~<i.l.-It is also shown how this algorithm can be extended to the case in which ~ is an algebraic multiset. A few applications are stated (among them, how to determine a reduced Grfbner basis of 3(,~) with respect to %i.1. without using Buchberger's algorithm).
New algorithms to perform both the generalizations due to Knuth [2] of the Robinson-Schensted cor... more New algorithms to perform both the generalizations due to Knuth [2] of the Robinson-Schensted correspondence and their inverse correspondences are given. 1. Preliminary definitions Let EE(O, l}; throughout this paper we shall consider two-line arrays such as b, bz ... b, CT= ((bi, ai)EN X N) a, a, '+. a, wherebiGbi.1 andbi=bi+l *ai < ai+ I + E. We use the term E-two-line array for such * Corresponding author.
The K-linear space of all n-linearly recursive functions (1.1) =evaluated differential forms) for... more The K-linear space of all n-linearly recursive functions (1.1) =evaluated differential forms) for which a zero-dimensional ideal ⊂ K x 1 x n is the largest ideal which is contained in the kernel of all of them turns out to be the orthogonal K-space ⊥ ⊂ K x 1 x n * of and is known as Macaulay's inverse system of. Making use of the antiderivative operator , the whole space of all differential forms can be endowed with a structure of K x 1 x n-module; with respect to finitely generated submodules of it (which we call Macaulay modules), we describe a dual analog of the Gröbner bases theory. The motivation for studying Macaulay modules has to be found mainly in multivariate interpolation problems and in the theory of polynomial bialgebras, though some application to algebraic geometry is not excluded.
Let K be a field; let ~mK" be a finite set and let 3(N)mK[xl ..... x,] be the ideal of ~. A purel... more Let K be a field; let ~mK" be a finite set and let 3(N)mK[xl ..... x,] be the ideal of ~. A purely combinatorial algorithm to obtain a linear basis of the quotient algebra K Ix1 ..... x,]/3(~) is given. Such a basis is represented by an n-dimensional Ferrers diagram of monomials which is minimal with respect to the inverse lexicographical order ~<i.l.-It is also shown how this algorithm can be extended to the case in which ~ is an algebraic multiset. A few applications are stated (among them, how to determine a reduced Grfbner basis of 3(,~) with respect to %i.1. without using Buchberger's algorithm).
New algorithms to perform both the generalizations due to Knuth [2] of the Robinson-Schensted cor... more New algorithms to perform both the generalizations due to Knuth [2] of the Robinson-Schensted correspondence and their inverse correspondences are given. 1. Preliminary definitions Let EE(O, l}; throughout this paper we shall consider two-line arrays such as b, bz ... b, CT= ((bi, ai)EN X N) a, a, '+. a, wherebiGbi.1 andbi=bi+l *ai < ai+ I + E. We use the term E-two-line array for such * Corresponding author.
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