North-East Lattice Paths with Few Collinear Vertices

Lineage and corrections

Corrects North-East Lattice Paths with Few Collinear Vertices →

Supersedes North-East Lattice Paths with Few Collinear Vertices →

Gerver and Ramsey, On certain sequences of lattice points (Pacific J. Math. 83, 1979) evidence for this event

Both bounds move, and the gap stays enormous: the lower bound rises from $\exp(\Omega(\log^2 k))$ to $\exp(\Omega(k^{1/3}))$ and the upper falls from $\exp(O(k^4))$ to $\exp(O(k^2))$, so $A(k)$ is still undetermined between an exponent of $k^{1/3}$ and one of $k^2$. The paper's own closing discussion argues its lower-bound construction is near the limit of the method and that beating it needs additional randomness, a sharper line-counting step, or a different model entirely. parent of this event

Barnoff and Bright, North-East lattice paths avoiding k collinear points via satisfiability (2026) evidence for this event

This event attributed to Samuel Korsky

North-East Lattice Paths with Few Collinear Vertices evidence for this event

Gerver, Long walks in the plane with few collinear points (Pacific J. Math. 83, 1979) evidence for this event

This event attributed to GPT-5.5 Pro

Lidbetter, Improved bound for the Gerver-Ramsey collinearity problem (Discrete Math., 2024) evidence for this event

VibeMathed record: North-East Lattice Paths with Few Collinear Vertices evidence for this event

North-East Lattice Paths with Few Collinear Vertices parent of this event