Powers of the Vandermonde Determinant Are Eventually Non-SNP

Monical, Tokcan and Yong conjectured that every fixed positive power of the Vandermonde determinant fails to have saturated Newton polytope in sufficiently many variables. For every even power $k \ge 4$ there is an explicit lattice point of the Newton polytope of $a_{\delta_k}^k$ with vanishing coefficient, obtained from a Dyson constant-term identity; the odd case follows by alternation, proving the conjecture.