It's so exciting to be back in Lisbon for CGTC3. Especially after missing it two years ago.
The first day (Tuesday, January 22) started off with some great talks. Here are some very brief summaries.
Richard Nowakowski: "What's happening in CGT (since 2010)"
Richard opened the meeting by speaking about new branches of CGT that have appeared this decade. His survey included explaining Misere and Scoring play, simultaneous moves, ties, placement games, and more. It was best summarized by his statement: "What did they [BCG] not think about because they didn't need to?"
Antoine Dailly: "Connected Subtraction Games on Graphs"
Antoine described a new game inspired by subtraction games. CSG(S) is a game on a graph where you may remove k connected vertices from G where k is in S and the resulting graph is still connected. His team has shown some nice periodicity results when appending paths to an initial graph.
Mike Fisher: "Beatty Games Big and Small"
Mike explained Beatty sequences, then talked about some new Beatty-based games, including two partizan subtraction games, octal games, and even infinite octal games. The talk name is from these subtraction games: big values occur if the subtraction sets are exactly the Beatty sequences and small values happen if you include 1 to both sets.
Carlos Pereira dos Santos: "Extended CGT"
Carlos considers adding infinity and negative infinity to the set of game options as terminal moves: infinity is an automatic win for left (and vice versa), no matter what else is going on in other parts of a game sum. (He motivated this by Atari Go.) He calls these types of game Race Games.
Marc Heinrich: "Partizan Subtraction Games"
Marc and his team made nice progress on partizan subtraction games. I did not know that outcome classes are periodic here, though values are not always! Marc showed that the sizes of the sets can be much less important that the size of the numbers in the set.
Bernhard von Stengel: "Computational Progress on the Catch-Up Game"
Bernhard described Catch-Up, a kind of scoring game that doesn't use alternating play; instead, whomever has the LOWER score gets to take the next turn. Bernhard showed a really cool method he found to solve this for big games, using the representation of prior choices as a binary address for the table of values being generated.
3 days ago