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A224913
Number of different nonisomorphic antimatroids on n labeled items.
1
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
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.
Yulia Kempner, Vadim E. Levit, Correspondence between two antimatroid algorithmic characterizations, arXiv:math/0307013 [math.CO], 2003.
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
KEYWORD
nonn,hard,more
AUTHOR
Przemyslaw Uznanski, Apr 19 2013
STATUS
approved