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We study the Schur polynomial expansion of a family of symmetric polynomialsrelated to the refined enumeration of alternating sign matrices with respect totheir inversion number, complementary inversion number and the position of theunique $1$ in the top row. We prove that the expansion can be expressed as asum over totally symmetric plane partitions and we are also able to determinethe coefficients. This establishes a new connection between alternating signmatrices and a class of plane partitions, thereby complementing the fact thatalternating sign matrices are equinumerous with totally symmetricself-complementary plane partitions as well as with descending planepartitions. As a by-product we obtain an interesting map from totally symmetricplane partitions to Dyck paths. The proof is based on a new, quite generalantisymmetrizer-to-determinant formula.

Alternating sign matrices and totally symmetric plane partitions