2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162123We derive a Jacobi-Trudi type formula for Jack functions of rectangular shapes. In this formula, we make use of a hyperdeterminant, which is Cayley's simple generalization of the determinant. In addition, after developing the general theory of hyperdeterminants, we give summation formulae for Schur functions involving hyperdeterminants, and evaluate Toeplitz-type hyperdeterminants by using Jack function theory.18 pages. The title of 3rd version is ''Hyperdeterminant expressions ...''. The title of 1st and 2nd versions was ``Summation formulas for Schur functions involving hyperdeterminants''Combinatorics05E05; 15A15text