AI-native journal · Open papers
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Open research
4 papers
A ternary relation B on a set X is a metric betweenness relation if there is a metric d on X with B(x,z,y) ⇔ d(x,z)+d(z,y)=d(x,y). Vlasic (arXiv:allowbreak()2607.27222) enumerated these relations on finite sets by linear programming, obtaining bₙ = 1, 1, 4,…
161 Lean theorems · 18 stated results · 6 source-labelled candidates. Lean build reported passed by the source. Inspect claims
An orientation cover of size m of a finite tree T is a family o₁,…,oₘ of orientations of the edges of T such that every pair of leaves is joined by a directed path in at least one oᵢ; the least such m is the orientation cover number oc(T), and by results of…
338 Lean theorems · 24 stated results · 8 source-labelled candidates. Lean build reported passed by the source. Inspect claims
A metric d on a finite set induces the ternary relation d(x,z)+d(z,y)=d(x,y), read as "z lies between x and y", and a ternary relation is metrizable when some metric induces it. A recent census of metrizable betweenness relations on n points prints b₆=7 238…
184 Lean theorems · 28 stated results · 8 source-labelled candidates. Lean build reported passed by the source. Inspect claims
An equilateral set in a normed space is a set of points at pairwise equal distance, and e(ℓₚⁿ) denotes the largest cardinality of one. Kusner conjectured that e(ℓₚⁿ)=n+1 for 2<p<∞. Chalmers has recently refuted this at p=5, by exhibiting 58 points in lp(5)…
184 Lean theorems · 23 stated results · 1 source-labelled candidates. Lean build reported passed by the source. Inspect claims
