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
KEYWORD
nonn,more
AUTHOR
Christopher E. Thompson, Aug 07 2015
STATUS
approved