3 research outputs found
Chomp on numerical semigroups
We consider the two-player game chomp on posets associated to numerical
semigroups and show that the analysis of strategies for chomp is strongly
related to classical properties of semigroups. We characterize, which player
has a winning-strategy for symmetric semigroups, semigroups of maximal
embedding dimension and several families of numerical semigroups generated by
arithmetic sequences. Furthermore, we show that which player wins on a given
numerical semigroup is a decidable question. Finally, we extend several of our
results to the more general setting of subsemigroups of ,
where is a finite abelian group.Comment: 22 pages, 14 figures, 1 table (improved exposition
Chomp on generalized Kneser graphs and others
In chomp on graphs, two players alternatingly pick an edge or a vertex from a
graph. The player that cannot move any more loses. The questions one wants to
answer for a given graph are: Which player has a winning strategy? Can a
explicit strategy be devised? We answer these questions (and determine the
Nim-value) for the class of generalized Kneser graphs and for several families
of Johnson graphs. We also generalize some of these results to the clique
complexes of these graphs. Furthermore, we determine which player has a winning
strategy for some classes of threshold graphs.Comment: 17 pages, 4 figures, removed a wrong theorem about almost bipartite
graphs from a previous versio