TY - JOUR
AU - Isserlis, L.
AB - 1. The reduction, of transvectants depends on the possibility of insert- ing between any two terms of a transvectant a series of others such that any two consecutive terms possess the property which is described technically as " adjacence." It is asserted without proof that this is possible by Gordan {Vorlesungen iiber Invariantentheorie, Zweiter Band, § 42, S. 44), by Clebsch (Biniire Formen, § 53, S. 185), and by Grace and Young (Algebra of Invariants, Art. 50, p. 51). In endeavouring to prove this possibility I have succeeded in giving a method of arranging the terms of any polar or transvectant in a single series, such that any two consecutive terms are in the technical sense " adjacent." The results, so far as I can express them in the space at my disposal, are as follows. In the following, numerical coefficients are immaterial and are omitted. Let D, denote an operator which polarizes powers of a only, with Sx regard to y, so that Then the ordered development of (-D +Z). ) is 1 2 jy J)r-\ T) T)r-2 T)'2 T)r 1Ji Ul, X/j xy> JJ\ J-^2' •••» iy and that of {D -\-D Y the same written in 
TI - On the Ordering of the Terms of Polars and Transvectants of Binary Forms
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s2-6.1.406
DA - 1908-01-01
UR - https://www.deepdyve.com/lp/wiley/on-the-ordering-of-the-terms-of-polars-and-transvectants-of-binary-cmS7fjszAw
SP - 406
EP - 409
VL - s2-6
IS - 1
DP - DeepDyve
ER -