Revista de la
Unión Matemática Argentina
Gotzmann monomials in four variables
Vittoria Bonanzinga and Shalom Eliahou
Volume 62, no. 1 (2021), pp. 67–93

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