Séminaire Lotharingien de Combinatoire, 95B.11 (2026), 12 pp.
Seunghun Lee and Eran Nevo
On an Extension Problem on the Moment Curve
Abstract.
We show that for 2≤d&le4, every finite geometric simplicial
complex Δ in Rd with vertices on the
moment curve can be extended to a triangulation T of the cyclic
polytope C where Δ, T and C all have the
same vertex set. Further, for d≥5 we construct complexes
Δ for which no such triangulations T exist.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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