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On Determinants of Symmetric Functions
Published online by Cambridge University Press: 20 January 2009
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The result of dividing the alternant |aαbβcγ…| by the simplest alternant |a0b1c2…| (the difference-product of a, b, c, …) is known to be a symmetric function expressible in two distinct ways, (1) as a determinant having for elements the elementary symmetric functions C, of a, b, c, …, (2) as a determinant having for elements the complete homogeneous symmetric functions Hr. For example
The formation of the (historically earlier) H-determinant is evident. The suffixes in the first row are the indices of the alternant; those of the other rows decrease by unit steps. This result is due to Jacobi.
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- Copyright © Edinburgh Mathematical Society 1927
References
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