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VIII.—The Theory of Alternants, from 1896 to 1917
Published online by Cambridge University Press: 15 September 2014
Extract
In the period which we have now reached the interest taken in the study of Alternants shows comparatively little sign of slackening, especially if the years given over to the War be taken into account. Close on fifty (50) writings, in six different languages and of various degrees of importance, fall to be considered.
One noteworthy feature of the collection is the exceptional number of the papers occupied with the investigation of Symmetric Functions: approximately a third of the whole may be so classified. It is also somewhat striking in connection therewith to note that this body of work has two quite independent sources, the one centring in a small East-Prussian town, the other confined mainly to a busy city in the State of New York.
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References
page 130 note * Cayley, A., “Note sur l'addition des fonctions elliptiques,” Crelle's Journ., xli, pp. 57–65Google Scholar; or Collected Math. Papers, i, pp. 540–549.
page 132 note * The reference made to Retali (Le Mat. pure ed appl., i, pp. 14–16) is unimportant.
page 133 note * Also, we may add, by at once putting c 1c 4, c 5, c 6 equal to 0.
page 133 note † See below, p. 147, under Muir, T. (1903).
page 134 note * Still simpler is a question put in the Math. Gaz., ii (1903), p. 363, in regard to an alternant equal to 
The equality given in the Educ. Times, lxvi (1913), p. 218, dates back to 1876 at least; and the set of equations dealt with in the American Math. Monthly, viii (1901–2), p. 266; ix, pp. 136–137, 162, is that known as Lagrange's (Hist., ii, p. 155).
page 135 note * Archiv (3), ix, pp. 113–143.
page 140 note * Educ. Times, lvi, p. 157.
page 143 note * This may be readily proved by multiplying the left-hand member by
or the right-hand member by
A similar result is that
page 147 note * Junge, G., Zur Hauptaufgabe der symmetrischen Funktionen. Dissert. Berlin, 1917.