학술저널
GENERATING FUNCTIONS FOR PLATEAUS IN MOTZKIN PATHS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 25, No. 3
-
2012.08475 - 489 (15 pages)
- 2
A plateau in a Motzkin path is a sequence of three steps: an up step, a horizontal step, then a down step. We ¯nd three di？？erent 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.
1. Forms for generating functions
2. Proof of results 1.1{1.3
3. Generalization to longer plateaus
4. Further generalizations and continued fraction expansions
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