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A Schur function identity related to the (-1)-enumeration of self-complementary plane partitions
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We give another proof for the (-1)-enumeration of self-complementary plane partitions with at least one odd side-length by specializing a certain Schur function identity. The proof is analogous to Stanley's proof for the ordinary enumeration. In addition, we obtain enumerations of 180-degree symmetric rhombus tilings of hexagons with a barrier of arbitrary length along the central line.
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Factorization of Schur polynomials twisted by roots of unity and a reciprocal pair
For s_λ(μ_t, z, z^{-1}), the evaluation is zero or a signed product of three hyperbolic sine factors read from the t-residue profile, for every t and every shape.
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