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On the number of terms in a simple algebraic form

Published online by Cambridge University Press:  24 October 2008

D. E. Littlewood
D. E. Littlewood
Affiliation:
University CollegeSwansea
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Extract

In a note in the April 1942 issue of these Proceedings, Hodge gives a formula for the number of independent terms in what he calls a k-connex, but while conjecturing its general validity he proves it only for very restricted cases. Its truth is here demonstrated in the general case.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 4 , November 1942 , pp. 394 - 396
Copyright
Copyright © Cambridge Philosophical Society 1942

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References

* Hodge, W. V. D, ‘A note on connexes’, Proc. Cambridge Phil. Soc. 38 (1942), 129–43.CrossRefGoogle Scholar

† In tensor calculus the word ‘contragredient’ is usual.

‡ Schur, I., ‘Über eine Klasse von Matrizen die sich einer gegebenen Matrix zuordnen lassen’, Inaugural Dissertation, Berlin (1901)Google Scholar; or see Littlewood, D. E., The theory of group characters and matrix representations of groups (Oxford, 1940)Google Scholar, Chapter x. This work will be referred to as G.C. See also Littlewood, D. E., ‘Polynomial concomitants and invariant matrices’, J. London Math. Soc. 11 (1936), 49, or G.C., 203.CrossRefGoogle Scholar

§ See G.C., Chapter x.

* Littlewood, D. E. and Richardson, A. R., ‘Immanants of some special matrices’, Quarterly J. Math. 5 (1934), 269.CrossRefGoogle Scholar See also ‘Some special S-functions and q-series’, Quarterly J. Math. 6 (1935), 184; or G.C., Chapter vii.Google Scholar

† See Turnbull, H. W., The theory of determinants, matrices and invariants, Chapter xvi (London and Glasgow, 1928).Google Scholar

‡ Schur, I., ‘Neue Anwendung der Integralrechnung auf Probleme der Invariantentheorie’, Sitzungsberichte Preuss. Akad. (1924), 189, 297, 346. Or see G.C. 236.Google Scholar