Analysis of straightening formula
The straightening formula has been an essential part of a proof showing that the set of standard bitableaux (or the set of standard monomials in minors) gives a free basis for a polynomial ring in a matrix of indeterminates over a field. The straightening formula expresses a nonstandard bitableau as...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000298 |
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| _version_ | 1832564934842515456 |
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| author | Devadatta M. Kulkarni |
| author_facet | Devadatta M. Kulkarni |
| author_sort | Devadatta M. Kulkarni |
| collection | DOAJ |
| description | The straightening formula has been an essential part of a proof showing that the set of
standard bitableaux (or the set of standard monomials in minors) gives a free basis for a polynomial ring in a matrix of indeterminates over a field. The straightening formula expresses a nonstandard bitableau as an integral linear cobmbination of standard bitableaux. In this paper we analyse the exchanges in the process of straightening a nonstandard pure tableau of depth two. We give precisely the number of steps required to straighten a given violation of a nonstandard tableau. We also characterise the violation which is eliminated in a single step. |
| format | Article |
| id | doaj-art-0f5b8cfa9df64d09a7d02a539b6d54e5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0f5b8cfa9df64d09a7d02a539b6d54e52025-02-03T01:09:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111224324910.1155/S0161171288000298Analysis of straightening formulaDevadatta M. Kulkarni0Department of Mathematics, Oakland University, Rochester Michigan 48063, USAThe straightening formula has been an essential part of a proof showing that the set of standard bitableaux (or the set of standard monomials in minors) gives a free basis for a polynomial ring in a matrix of indeterminates over a field. The straightening formula expresses a nonstandard bitableau as an integral linear cobmbination of standard bitableaux. In this paper we analyse the exchanges in the process of straightening a nonstandard pure tableau of depth two. We give precisely the number of steps required to straighten a given violation of a nonstandard tableau. We also characterise the violation which is eliminated in a single step.http://dx.doi.org/10.1155/S0161171288000298bitableauxstandard bitableauxunitableaux of pure length and depth twomonomials in minorsstraightening formulaoddity functionviolationgood violationnumber of steps to straighten a nonstandard unitableau. |
| spellingShingle | Devadatta M. Kulkarni Analysis of straightening formula International Journal of Mathematics and Mathematical Sciences bitableaux standard bitableaux unitableaux of pure length and depth two monomials in minors straightening formula oddity function violation good violation number of steps to straighten a nonstandard unitableau. |
| title | Analysis of straightening formula |
| title_full | Analysis of straightening formula |
| title_fullStr | Analysis of straightening formula |
| title_full_unstemmed | Analysis of straightening formula |
| title_short | Analysis of straightening formula |
| title_sort | analysis of straightening formula |
| topic | bitableaux standard bitableaux unitableaux of pure length and depth two monomials in minors straightening formula oddity function violation good violation number of steps to straighten a nonstandard unitableau. |
| url | http://dx.doi.org/10.1155/S0161171288000298 |
| work_keys_str_mv | AT devadattamkulkarni analysisofstraighteningformula |