Obstructions to combinatorial formulas for plethysm

摘要: Motivated by questions of Mulmuley and Stanley we investigate quasi-polynomials arising in formulas for plethysm. We demonstrate, on the examples $S^3(S^k)$ $S^k(S^3)$, that these need not be counting functions inhomogeneous polytopes dimension equal to degree quasi-polynomial. It follows are not, general, lattice points any scaled convex bodies, even when restricted single rays. Our results also apply special rectangular Kronecker coefficients.