The Smith normal form of a specialized Giambelli-type matrix
| Autor: | Matthew H.Y. Xie, Alice L. L. Gao, Arthur L. B. Yang |
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| Rok vydání: | 2018 |
| Předmět: |
Mathematics::Combinatorics
Applied Mathematics 010102 general mathematics Block matrix 0102 computer and information sciences 01 natural sciences Square matrix Matrix similarity Combinatorics Matrix (mathematics) Mathematics::Algebraic Geometry 010201 computation theory & mathematics Matrix function FOS: Mathematics 05E05 Mathematics - Combinatorics Symmetric matrix Combinatorics (math.CO) Nonnegative matrix 0101 mathematics Mathematics Smith normal form |
| Zdroj: | Advances in Applied Mathematics. 92:1-16 |
| ISSN: | 0196-8858 |
| DOI: | 10.1016/j.aam.2017.06.003 |
| Popis: | In the study of determinant formulas for Schur functions, Hamel and Goulden introduced a class of Giambelli-type matrices with respect to outside decompositions of partition diagrams, which unify the Jacobi-Trudi matrices, the Giambelli matrices and the Lascoux-Pragacz matrices. Stanley determined the Smith normal form of a specialized Jacobi-Trudi matrix. Motivated by Stanley's work, we obtain the Smith normal form of a specialized Giambelli matrix and a specialized Lascoux-Pragacz matrix. Furthermore, we show that, for a given partition, the Smith normal form of any specialized Giambelli-type matrix can be obtained from that of the corresponding specialization of the classical Giambelli matrix by a sequence of stabilization operations. 15 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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