Name
Abstract | ||
|---|---|---|
In the third volume of his book on the art of computer programming, Knuth has refined a sorting procedure originated by Robinson and Schensted. By employing a modification of this procedure, in this paper we show that the Straightening Law of Doubilet-Rota-Stein is not valid in the case of ‘higher dimensional’ matrices. In greater detail: In the classical two-dimensional case, the said Law says that the standard monomials in the minors of a (rectangular) matrix X , which correspond to standard bitableaux, form a vector space basis of the polynomial ring K [ X ] in the indeterminate entries of X over the coefficient field K . Now we may ask what happens to this when we consider ‘higher dimensional’ matrices by using cubical, 4-way,…, q -way determinants which were already introduced by Cayley in 1843. In the present paper, as a consequence of the Robinson-Schensted-Knuth correspondence, we show that, for q > 2, the standard monomials in the multiminors of the multimatrix X do not span the polynomial ring K [ X ]; in a forthcoming paper it will be shown that they are linearly independent over K . |
Year | DOI | Venue |
|---|---|---|
1991 | 10.1016/0012-365X(91)90350-B | Discrete Mathematics |
Keywords | DocType | Volume |
generalized rodeletive correspondence,generalized roinsertive correspondence | Journal | 90 |
Issue | ISSN | Citations |
2 | Discrete Mathematics | 2 |
PageRank | References | Authors |
0.78 | 3 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shreeram S. Abhyankar | 1 | 23 | 6.93 |
| Sanjeevani B. Joshi | 2 | 2 | 0.78 |