Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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GENERATING FUNCTIONS FOR PLATEAUS IN MOTZKIN PATHS

  • Drake, Dan (Department of Mathematical Sciences Korea Advanced Institute of Science and Technology) ;
  • Gantner, Ryan (Department of Mathematical and Computing Sciences St. John Fisher College)
  • Published : 2012.08.15
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Abstract

A plateau in a Motzkin path is a sequence of three steps: an up step, a horizontal step, then a down step. We find three different forms for the bivariate generating function for plateaus in Motzkin paths, then generalize to longer plateaus. We conclude by describing a further generalization: a continued fraction form from which one can easily derive new multivariate generating functions for various kinds of path statistics. Several examples of generating functions are given using this technique.

Keywords

References

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