A379887 Number of rational polygons with denominator at most n having exactly one lattice point in their interior, up to equivalence.

16, 5145, 924042, 101267212, 8544548186

Offset

1,1

Comments

A379894 counts the polygons with the extra condition that the vertices are primitive. Both are in Classification 5.6 of the article by Bohnert and Springer.

An algorithm to compute a(n) was given by Timo Hummel in his dissertation. His final number for n = 3 (given in Theorem 12.1) was however slightly off.

Links

Table of n, a(n) for n=1..5.

Martin Bohnert and Justus Springer, Classifying rational polygons with small denominator and few interior lattice points, arXiv:2410.17244 [math.CO], 2024.

Martin Bohnert and Justus Springer, Rational polygons with exactly one interior lattice point [Data set]. Zenodo.

Daniel Hättig, Jürgen Hausen, and Justus Springer, Classifying log del Pezzo surfaces with torus action, arXiv:2302.03095 [math.AG], 2023.

Daniel Hättig, Lattice Polygons and Surfaces with Torus Action, Dissertation (2023).

Timo Hummel, Automorphisms of rational projective K*-surfaces, Dissertation (2021).

Justus Springer, RationalPolygons.jl (Version 1.1.0) [Computer software], 2024.

Example

For n = 1, there are 16 lattice polygons with exactly one interior lattice point, which are the 16 reflexive lattice polygons.

Crossrefs

Cf. A379894, A322343, A145581, A371917.

Sequence in context: A123280 A289904 A375104 * A181028 A258583 A337796

Adjacent sequences: A379884 A379885 A379886 * A379888 A379889 A379890

Keyword

nonn,more

Author

Justus Springer, Jan 05 2025

Status

approved