Gotzmann monomials in four variables
It is a widely open problem to determine which monomials in the n-variable polynomial ring K[x_1,...,x_n] over a field K have the Gotzmann property, i.e. induce a Borel-stable Gotzmann monomial ideal. Since 2007, only the case n ≤ 3 was known. Here we solve the problem for the case n = 4. The solution involves a surprisingly intricate characterization.