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18

COMBINATORICS
2000

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Continued Fractions and Catalan Problems

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Continued Fractions and Catalan Problems

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We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to an ordered-tree problem and their generating functions also expressed as a continued fraction. Among these problems is the enumeration of (132)-pattern avoiding permutations that have a given number of increasing patterns of length k. This extends and illuminates a result of Robertson, Wilf and Zeilberger for the case k = 3.

Mahendra Jani, Robert G. Rieper

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COMBINATORICS 2000 | Continued Fraction | Generating Functions | Several Catalan Problems |

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Added	17 Dec 2010
Updated	17 Dec 2010
Type	Journal
Year	2000
Where	COMBINATORICS
Authors	Mahendra Jani, Robert G. Rieper

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