Geodesic
Enumerative properties of posets corresponding to a certain class of games of no strategy
Journal of integer sequences, Tome 20 (2017) no. 5
In this paper, we consider a game beginning with a multiset of elements from a group. Each move replaces two elements with their sum. This is a game of no strategy and can be modeled by a graded poset with the rank of a node equal to the cardinality of its multiset. We study the enumerative properties of certain variations of this game, such as the number of ways to play them and their numbers of end states. This leads to several new sequences, as well as new interpretations of classic sequences such as those found in the Catalan and Motzkin triangles.
Classification : 05A15
Keywords: poset, game of no strategy, Catalan triangle, Motzkin triangle, recursion, bijection 
@article{JIS_2017__20_5_a6,
     author = {Ji,  Caleb},
     title = {Enumerative properties of posets corresponding to a certain class of games of no strategy},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {5},
     zbl = {1361.05011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_5_a6/}
}
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Ji,  Caleb. Enumerative properties of posets corresponding to a certain class of games of no strategy. Journal of integer sequences, Tome 20 (2017) no. 5. http://geodesic.mathdoc.fr/item/JIS_2017__20_5_a6/