Journal article
Multivariable Vandermonde determinants, amalgams of matrices and Specht modules
- Abstract:
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Using results of Fayers on the structure of Specht modules, we prove two different formulae for the determinant of a matrix which is 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Version of record, pdf, 534.4KB, Terms of use)
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- Publisher copy:
- 10.1016/j.jalgebra.2025.03.040
Authors
- Publisher:
- Elsevier
- Journal:
- Journal of Algebra More from this journal
- Volume:
- 678
- Pages:
- 253-278
- Publication date:
- 2025-04-11
- Acceptance date:
- 2024-12-07
- DOI:
- EISSN:
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1090-266X
- ISSN:
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0021-8693
- Language:
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English
- Keywords:
- Pubs id:
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2119438
- Local pid:
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pubs:2119438
- Deposit date:
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2025-04-23
- ARK identifier:
Terms of use
- Copyright holder:
- Francis Brown
- Copyright date:
- 2025
- Rights statement:
- © 2025 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).
- Licence:
- CC Attribution (CC BY)
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