A 7-vertex tournament whose Sperner capacity exceeds the order of its largest transitive subtournament: T₇, induced by the Paley tournament on 23 vertices on 0, 1, 2, 3, 9, 14, 18, has t = 4 and √18 ≤ C ≤ 5; every tournament on at most six vertices has C = t, so seven is the least order
A Lean 4 development on the capacity of digraphs in the sense of Alon (1998): w(R^n) is the largest set of words of length n such that every ordered pair of distinct words has a coordinate carrying an arc from the first to the second, and C(R) is the supremum of w(R^n)^(1/n), which equals the limit; for a tournament T, t(T) is the order of its largest transitive subtournament and t(T) ≤ C(T). Conjecture 1.1 of Alon's paper, attributed to Körner and Simonyi, asserts C(T) = t(T) for every tournament; Alon disproved it with a random construction and with the Paley tournament on 67 vertices, and…
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