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

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.

Links

Table of n, a(n) for n=0..4.

Crossrefs

Cf. A065401 (all games), also A000372 for antichain conjecture.

Sequence in context: A240317 A145075 A058924 * A154731 A201346 A174663

Adjacent sequences: A260967 A260968 A260969 * A260971 A260972 A260973

Keyword

nonn,more

Author

Christopher E. Thompson, Aug 07 2015

Status

approved