Stable equivalence over symmetric functions (Q2583629)

Summary: By using cutting strips and transformations on outside decompositions of a skew diagram, we show that the Giambelli-type matrices for a given skew Schur function are stably equivalent to each other over symmetric functions. As a consequence, the Jacobi-Trudi matrix and the transpose of the dual Jacobi-Trudi matrix are stably equivalent over symmetric functions. This leads to an affirmative answer to a question proposed by \textit{G. Kuperberg} [Kasteleyn cokernels, Electron. J. Comb. 9, Research paper R29 (2002; Zbl 1006.05005)].