Journal of Integer Sequences, Vol. 20 (2017), Article 17.5.1

Enumerative Properties of Posets Corresponding to a Certain Class of Games of No Strategy

Caleb Ji
Department of Mathematics
Washington University in St. Louis
1 Brookings Drive
St. Louis, MO 63130


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.

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(Concerned with sequences A000097 A000108 A001006 A001263 A002846 A014138 A026300 A117142 A117143 A140144 A194621 A276027 A276028 A276029 A276030 A276031 A276032 A276033.)

Received August 26 2016; revised versions received December 30 2016; March 20 2017. Published in Journal of Integer Sequences, March 25 2017.

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