All passable games are realizable as monotone set coloring games
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910976562954240 |
|---|---|
| author | Demer, Eric Selinger, Peter Wang, Kyle |
| author_facet | Demer, Eric Selinger, Peter Wang, Kyle |
| contents | The class of passable games was recently introduced by Selinger as a class of combinatorial games that are suitable for modelling monotone set coloring games such as Hex. In a monotone set coloring game, the players alternately color the cells of a board with their respective color, and the winner is determined by a monotone function of the final position. It is easy to see that every monotone set coloring game is a passable combinatorial game. Here we prove the converse: every passable game is realizable, up to equivalence, as a monotone set coloring game. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_10351 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | All passable games are realizable as monotone set coloring games Demer, Eric Selinger, Peter Wang, Kyle Combinatorics 91A46 The class of passable games was recently introduced by Selinger as a class of combinatorial games that are suitable for modelling monotone set coloring games such as Hex. In a monotone set coloring game, the players alternately color the cells of a board with their respective color, and the winner is determined by a monotone function of the final position. It is easy to see that every monotone set coloring game is a passable combinatorial game. Here we prove the converse: every passable game is realizable, up to equivalence, as a monotone set coloring game. |
| title | All passable games are realizable as monotone set coloring games |
| topic | Combinatorics 91A46 |
| url | https://arxiv.org/abs/2111.10351 |