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Note on Dual Symmetric Functions

Published online by Cambridge University Press:  20 January 2009

A. C. Aitken
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In an earlier paper, which this note is intended to supplement and in some respects improve, the writer gave a general theorem of duality relating to isobaric determinants with elements Cr and Hr, the elementary and the complete homogeneous symmetric functions of a set of variables. The result was shewn to include as special cases the dual forms of “bi-alternant” symmetric functions given by Jacobi and Naegelsbach, as well as two equivalent forms of isobaric determinant used by MacMahon as a generating function in an important problem of permutations.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 2 , Issue 3 , January 1931 , pp. 164 - 167
Copyright
Copyright © Edinburgh Mathematical Society 1931

References

page 164 note 1 See Muir's History of Determinants, 1, 341, 2, 146.Google Scholar

page 164 note 2 Combinatory Analysis (Cambridge, 1915), 1, 205.Google Scholar

page 166 note 1 It has seemed more convenient to use ascending partitions, and to reverse the order in conjugate compositions from MacMahon's ; the triple formulation is then simple and consistent.

page 166 note 2 J. für Math., 132 (1907), 159, 161.Google Scholar