Rectangular Kronecker coefficients and plethysms in geometric complexity theory

摘要: Abstract We prove that in the geometric complexity theory program vanishing of rectangular Kronecker coefficients cannot be used to superpolynomial determinantal lower bounds for permanent polynomial. Moreover, we positivity a large class partitions where side lengths rectangle are at least quadratic length partition. also compare with their corresponding plethysm coefficients, which leads new bound coefficients. saturation semigroup is trivial, show stretching factor 2 long first row, and completely classify limit were introduced by Manivel 2011.