login
A260970
Number of hereditarily transitive normal play partisan games born on or before day n.
0
1, 4, 18, 176, 11363
OFFSET
0,2
COMMENTS
A game is transitive if any position reached by any number of consecutive moves by one player can be reached in a single move by that player. It is hereditarily transitive if it and all its followers are transitive.
The hereditarily transitive games born by day n form a distributive lattice whose Hasse diagram is planar. It is conjectured (known for n<=3) that the number of antichains in this lattice is 2^A000372(n)-2.
Aaron Siegel attributes the values up to a(3) to Angela Siegel, and a(4) to Neil McKay.
REFERENCES
Aaron N. Siegel, Combinatorial Game Theory, AMS Graduate Texts in Mathematics Vol 146 (2013), p. 158.
CROSSREFS
Cf. A065401 (all games), also A000372 for antichain conjecture.
Sequence in context: A240317 A145075 A058924 * A154731 A201346 A174663
KEYWORD
nonn,more
AUTHOR
STATUS
approved