The Boolean algebra Bn, partitioned into chains by the order-matchings that Lemma 4.5 extracts from nonzero determinants. Every chain crosses the middle level, so an antichain has at most C(n,⌊n/2⌋) elements.
Made for Math 372: Combinatorics at Reed College, fall 2026. The chains come from order-matchings Pi → Pi+1 (i < n/2) and Pi+1 → Pi (i ≥ n/2), each read off a nonzero term in the determinant of a square submatrix of the up-operator, as in Lemma 4.5 of Stanley's Algebraic Combinatorics; the bracketing rule is de Bruijn–Tengbergen–Kruyswijk's. Part of e-infinity.space/viz.