Gaoqiang Liu

Single-step decreases in the three-row Chomp diagonal sequence: A uniform bound below one half

Let dn be the unique first-row length for which (dn, n, n) is a losing position in three-row Chomp, and let gn = max{0, dn − dn+1}. For every integer n ≥ 6, we prove gn ≤ 83n/168 and the signed bound dn − dn+1 ≤ 83n/168 − 125/84. More precisely, the signed upper bound is 83n/168...

Near-rectangular P-positions in three-row Chomp with deficit at most six

We classify the losing positions (n,n,n-g) in three-row Chomp for every integer n>g and 1<=g<=6. There are exactly eight such positions. The proof combines a counting bound for the row at which a value becomes constant with a uniform bound obtained from Zeilberger's published low...

A Computer-Assisted Proof of a First-Player Win in Infinite Freestyle Gomoku

We present a computer-assisted proof that the first player wins freestyle Gomoku on the infinite integer lattice. Players alternately occupy an empty lattice point, and a consecutive run of at least five stones in any of four directions wins immediately; neither player has forbid...

A Computer-Assisted Proof of a First-Player Win in Infinite Freestyle Gomoku

We present a computer-assisted proof that the first player wins freestyle Gomoku on the infinite integer lattice. Players alternately occupy an empty lattice point, and a consecutive run of at least five stones in any of four directions wins immediately; neither player has forbid...

A Computer-Assisted Proof of a First-Player Win in Infinite Freestyle Gomoku

We present a computer-assisted proof that the first player wins freestyle Gomoku on the infinite integer lattice. Players alternately occupy an empty lattice point, and a consecutive run of at least five stones in any of four directions wins immediately; neither player has forbid...