Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2604.20390 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918461344579584 |
|---|---|
| author | Brown, Francis |
| author_facet | Brown, Francis |
| contents | Using results of Fayers on the structure of Specht modules, we prove two different formulae for the determinant of matrices which are obtained by amalgamating the entries of two smaller matrices. In particular, this gives formulae for multivariable Vandermonde determinants as a sum of completely factorising terms, each of which is a Vandermonde determinant in fewer variables. As an application, we deduce an elementary proof of the multiplicativity of the transfinite diameter for products of compact sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20390 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multivariable Vandermonde determinants, amalgams of matrices and Specht modules Brown, Francis Representation Theory Combinatorics Group Theory 15A15, 20C30, 05E10, 32U20 Using results of Fayers on the structure of Specht modules, we prove two different formulae for the determinant of matrices which are obtained by amalgamating the entries of two smaller matrices. In particular, this gives formulae for multivariable Vandermonde determinants as a sum of completely factorising terms, each of which is a Vandermonde determinant in fewer variables. As an application, we deduce an elementary proof of the multiplicativity of the transfinite diameter for products of compact sets. |
| title | Multivariable Vandermonde determinants, amalgams of matrices and Specht modules |
| topic | Representation Theory Combinatorics Group Theory 15A15, 20C30, 05E10, 32U20 |
| url | https://arxiv.org/abs/2604.20390 |