Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-09T22:28:24.988Z Has data issue: false hasContentIssue false
  • English
  • Français

A Type of Alternant

Published online by Cambridge University Press:  20 January 2009

F. W. Ponting
F. W. Ponting
Affiliation:
Department of Mathematics, University of Aberdeen.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We define

where ap ≠ aq when p ≠ q. If N = Σλi, then the partition (λ1, λ2, …, λn) of N with λ1 ≥ λ2 ≥ … ≥ λn is denoted by (λ) and we set

All partitions will be in descending order and the usual notation for repeated parts will be used.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 1 , October 1953 , pp. 20 - 27
Copyright
Copyright © Edinburgh Mathematical Society 1953

References

REFERENCES

Littlewood, D. E., Theory of Group Characters (Oxford, 1940).Google Scholar
Hirsch, K. A., “A note on Vandermonde's determinant”, Journal London Math. Soc., 24 (1949), 144–5.Google Scholar
Aitken, A. C., Determinants and Matrices (5th ed., Edinburgh, 1948).Google Scholar
Aitken, A. C. “On determinants of symmetric functions”, Proc. Edinburgh Math. Soc. (2) 1 (1929), 55.CrossRefGoogle Scholar
Aitken, A. C. “Note on dual symmetric functions”, Proc. Edinburgh Math. Soc. (2), 2 (1931), 164.CrossRefGoogle Scholar
Aitken, A. C. “The monomial expansion of determinantal symmetric functions”, Proc. Royal Soc. Edinburgh (A), 61 (1941-1943), 300–310.Google Scholar
Mitchell, O. H., “Note on determinants of powers”, American Journal Math., 4 (1881)) 341–4.CrossRefGoogle Scholar
Foulkes, H. O., “Modified bialternants and symmetric function identities”, Journal London Math. Soc., 25 (1950), 268–75Google Scholar