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Revision History for A187015 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
A187015
The number of different classes of 2-dimensional convex lattice polytopes having volume n/2 up to unimodular equivalence.
(history; published version)
#41 by Michael De Vlieger at Wed Oct 11 08:42:33 EDT 2023
STATUS

proposed

approved

#40 by Andrey Zabolotskiy at Wed Oct 11 06:34:11 EDT 2023
STATUS

editing

proposed

#39 by Andrey Zabolotskiy at Wed Oct 11 06:34:07 EDT 2023
LINKS

Gabriele Balletti, <a href="https://github.com/gabrieleballetti/small-lattice-polytopes">Dataset of "small" lattice polytopes</a> (The . Beware that the vertices are not always listed in sorted in order around the polygon boundary (clockwise or counterclockwise order in his list.).

STATUS

proposed

editing

#38 by Andrey Zabolotskiy at Wed Oct 11 06:31:11 EDT 2023
STATUS

editing

proposed

#37 by Andrey Zabolotskiy at Wed Oct 11 06:27:06 EDT 2023
LINKS

Gabriele Balletti, <a href="https://doi.org/10.1007/s00454-020-00187-y">Enumeration of lattice polytopes by their volume</a>. , Discrete Comput. Geom., 65 (2021), 1087-1122; arXiv:<a href="https://arxiv.org/abs/1811.03357">1103.0103</a> [math.CO], 2018.

Discussion
Wed Oct 11
06:31
Andrey Zabolotskiy: Okay, we are happy now, I guess. Thank you for bringing up this confusing point.
#36 by Andrey Zabolotskiy at Wed Oct 11 06:26:24 EDT 2023
LINKS

Gabriele Balletti, <a href="https://arxivdoi.org/abs/181110.033571007/s00454-020-00187-y">Enumeration of lattice polytopes by their volume</a>, . Discrete Comput. Geom., 65 (2021), 1087-1122; arXiv:<a href="https://arxiv.org/abs/1811.03357">1103.0103 </a> [math.CO], 8 Nov 2018.

CROSSREFS

Cf. A126587, A003051 (triangles only), A322343, A366409.

#35 by Andrey Zabolotskiy at Wed Oct 11 06:24:08 EDT 2023
NAME

The number of different classes of 2-dimensional convex lattice polytopes having volume n/2 of their convex hull up to unimodular equivalence.

LINKS

Gabriele Balletti, <a href="https://github.com/gabrieleballetti/small-lattice-polytopes">Dataset of "small" lattice polytopes</a> (The vertices are not always sorted in clockwise or counterclockwise order in his list.)

EXTENSIONS

Name corrected by Hugo Pfoertner, Oct 11 2023

STATUS

proposed

editing

#34 by Hugo Pfoertner at Wed Oct 11 04:55:20 EDT 2023
STATUS

editing

proposed

Discussion
Wed Oct 11
05:14
Andrey Zabolotskiy: No, I don't think his data includes non-convex polytopes. Vertices are just not in order.
05:36
Hugo Pfoertner: But that's a bad trap, because what software should be used to display and evaluate these structures? The same problem also occurs in Balletti's "smooth" data, and in particular the "smooth" condition is no longer true after a rearrangement. But that's a bad trap, because what software should be used to display and evaluate these structures? The same problem also occurs in Balletti's "smooth" data, and in particular the "smooth" condition is no longer true after a rearrangement. See also the draft of A366409. Take a look at No. 41 in https://github.com/gabrieleballetti/small-lattice-polytopes/blob/master/data/smooth/2_polytopes.txt . See also the draft of A366409.
05:38
Hugo Pfoertner: Sorry for repeated parts in last message.
05:45
Andrey Zabolotskiy: What about No. 41? It's convex (if the vertices are arranged in the certain order).
I agree that this is a possible source of confusion, and Günter successfully mitigates it by the comment: (The vertices are not always sorted in clockwise or counterclockwise order in his list.)
We can add the same comment here.
05:46
Andrey Zabolotskiy: As for the software, I'm pretty sure any of us can write a program that sorts the vertices of a convex polygons in, say, counterclockwise order.
06:10
Hugo Pfoertner: I'm sorry; I hadn't seen Guenter's changes to the new sequence today when I wrote the discussion post here. An analogous comment on Balletti's data in the present sequence would certainly be useful, otherwise other people might also fall into this trap. Of course, no new software is needed for this. Mma's ConvexHullMesh[] does this.
#33 by Hugo Pfoertner at Wed Oct 11 04:53:42 EDT 2023
EXTENSIONS

Name corrected by Hugo Pfoertner, Oct 11 2023

#32 by Hugo Pfoertner at Wed Oct 11 04:37:21 EDT 2023
NAME

The number of different classes of 2-dimensional convex lattice polytopes having volume n/2 of their convex hull up to unimodular equivalence.

STATUS

approved

editing

Discussion
Wed Oct 11
04:52
Hugo Pfoertner: I have a strong suspicion that the current name does not describe what is shown in Balletti's data. Or is e.g. pol=Polygon[{{0,0},{1,0},{0,3},{2,-5},{-1,4},{-1,3}}]  (No. 67 in v12.txt) seen as a convex polygon? Mma. returns the area 31/12, and only Area[ConvexHullMesh[pol]] returns the area 12/2=6.

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