Open Access Te Herenga Waka-Victoria University of Wellington
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Towards the Calculation of Jack Polynomials

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posted on 2021-11-07, 23:42 authored by Roberts, Leigh Alan

Jack polynomials are useful in mathematical statistics, but they are awkward to calculate, and their uses have chiefly been theoretical. In this thesis a determinantal expansion of Jack polynomials in elementary symmetric polynomials is found, complementing a recent result in the literature on expansions as determinants in monomial symmetric functions. These results offer enhanced possibilities for the calculation of these polynomials, and for finding workable approximations to them. The thesis investigates the structure of the determinants concerned, finding which terms can be expected to dominate, and quantifying the sparsity of the matrices involved. Expressions are found for the elementary and monomial symmetric polynomials when the variates involved assume the form of arithmetic and geometric progressions. The latter case in particular is expected to facilitate the construction of algorithms suitable for approximating Jack polynomials.


Copyright Date


Date of Award



Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline

Statistics and Operations Research

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level


Degree Name

Doctor of Philosophy

Victoria University of Wellington Item Type

Awarded Doctoral Thesis



Victoria University of Wellington School

School of Mathematics, Statistics and Computer Science


Vere-Jones, David