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Source. D. Burt, E. Goldstein, S. Manski, S. J. Miller, E. A. Palsson and H. Suh, Crescent configurations, arXiv:1509.07220v1 [math.CO] (24 September 2015); Remark 3.1 on p. 4. The copy read is identified on the source card.

Read depth. Claims checked: the remark was read clause by clause on the page images. The paper gives no code, no description of the region beyond its size and shape, and no data, so the search was not reproduced. Nothing here is independently reviewed.

Statement

Remark 3.1 (p. 4). Using a parallel computing cluster, the authors searched a hexagonal region of $91$ points of the triangular lattice exhaustively for a crescent configuration with $n=9$ (in the plane, in the sense of Definition 1.2) and found none. The remark adds that their naive implementation needed more than $900$ hours of computation at this size, and that searching a much larger region needs better techniques.

The remark follows the paper's open questions of Section 3 (pp. 3--4), whether planar constructions exist for $n\ge9$ and whether they can be found on the triangular lattice, where constructions for $n<9$ are known.

Proof pointer

A computational report; the paper gives no further detail of the search.

Dependencies

Definitions 1.1 and 1.2 of the same paper.

Bears on

• Problem 217: the search excludes nine-point examples inside one 91-point region of the triangular lattice only; it does not exclude a nine-point example elsewhere on the lattice or off it, and the case $n=9$ stays open.