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A224913 Number of different nonisomorphic antimatroids on n labeled items. 1


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

%N Number of different nonisomorphic antimatroids on n labeled items.

%C 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.

%C 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.

%H D. Eppstein, <a href="https://11011110.github.io/blog/2006/06/18/reverse-search-for.html">Reverse search for antimatroids</a>.

%H Yulia Kempner, Vadim E. Levit, <a href="http://arXiv.org/abs/math/0307013">Correspondence between two antimatroid algorithmic characterizations</a>, arXiv:math/0307013 [math.CO], 2003.

%H P. Uznanski <a href="http://paracombinatorics.wordpress.com/2013/04/19/enumeration-of-antimatroids-part-iv/">Enumeration of antimatroids</a>

%e 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.

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

%K nonn,hard,more

%O 0,3

%A _Przemyslaw Uznanski_, Apr 19 2013

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Last modified February 24 17:17 EST 2020. Contains 332209 sequences. (Running on oeis4.)