A260970 Number of hereditarily transitive normal play partisan games born on or before day n.

1, 4, 18, 176, 11363

Offset: 0

Author

Christopher E. Thompson, Aug 07 2015

Keywords

• nonn
• more

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.