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John R. Stembridge works on algebraic combinatorics, representation theory, Coxeter groups and symmetric functions. His Michigan profile also identifies computational methods in algebra as a focus.^[ref]

With Richard P. Stanley, he studied immanants of matrices associated with the Jacobi–Trudi identity. An immanant replaces the sign character in a determinant by another symmetric group character. Their paper proves special cases of stronger positivity conjectures and connects the calculation with cycle structure of permutations having restricted positions.^[ref]

By Richard P. Stanley and John R. Stembridge. Journal of Combinatorial Theory, SeriesA62,261–279. Author-hosted primary article: math.mit.edu/~rstan/pubs/pubfiles/87.pdf

§1, equation(1.1), defines the Jacobi-Trudi matrix and its Schur determinant. §3, printed page270, explicitly fixes the unsigned forgotten-function convention, in contrast to the signed convention used by some sources.