A260968 Number of all-small normal play partisan games born on or before day n.

1, 2, 7, 67, 534483

Offset: 0

Author

Christopher E. Thompson, Aug 06 2015

Keywords

• nonn
• more

Comments

A game is all-small if it and all its followers other than 0 have options for both players, or equivalently (under normal play rules) if it and all its followers are infinitesimal. "All-small" is the traditional term, although Aaron Siegel prefers "dicotic", attributed to Michael Weimerskirch.

The all-small games born by day n form a distributive lattice if additional minimal and maximal elements are added.

The values up to a(4) are due to Aaron Siegel, computed using cgsuite.

References

• Aaron N. Siegel, Combinatorial Game Theory, AMS Graduate Texts in Mathematics Vol 146 (2013), p. 158.

Links

• David Wolfe, On day n, pp. 125-131 in Games of No Chance 3, MSRI Publications 56, Cambridge, 2009.

Crossrefs

Cf. A065401 (all games), A260967 (infinitesimal games).