A224913 Number of different nonisomorphic antimatroids on n labeled items.

1, 1, 2, 6, 34, 672, 199572, 12884849614

Offset

0,3

Comments

See link for software to generate the sequence. The next item (for n=8) should be roughly 2^63 and seems hopeless without more mathematics.

Antimatroids are a subset of greedoids, usually defined either in terms of set systems, as David Eppstein does in his tree searches, or in terms of formal languages. The two are equivalent, as discussed in Kempner and Levit.

Links

Table of n, a(n) for n=0..7.

Kira Adaricheva and Arav Agarwal, Representation of convex geometries of convex dimension 3 by spheres, arXiv:2308.07384 [math.CO], 2023.

Domenico Cantone, Jean-Paul Doignon, Alfio Giarlotta, and Stephen Watson, Resolutions of Convex Geometries, arXiv:2103.01581 [math.CO], 2021.

D. Eppstein, Reverse search for antimatroids.

Yulia Kempner, Vadim E. Levit, Correspondence between two antimatroid algorithmic characterizations, arXiv:math/0307013 [math.CO], 2003.

P. Uznanski Enumeration of antimatroids

Example

The three antimatroids on the two items 0 and 1 are (a) {},{0},{0,1}, (b) {},{1},{0,1} and (c) {},{0},{1},{0,1}, out of which (a) and (b) are isomorphic, leaving (a)/(b) and (c) as two nonisomorphic antimatroids.

Crossrefs

Cf. A119770 (counts antimatroids, not taking symmetries into account).

Sequence in context: A317080 A075272 A353536 * A327038 A228931 A101262

Adjacent sequences: A224910 A224911 A224912 * A224914 A224915 A224916

Keyword

nonn,hard,more

Author

Przemyslaw Uznanski, Apr 19 2013

Status

approved