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math.CO2000
Valleyless Sequences
Robert G. Rieper, Melkamu Zeleke
Valleyless sequences of finite length and maximum entry occur in tree enumeration problems and provide an interesting correspondence between permutations and compositions.…
math.CO2000
The Imbedding Sum of a Graph
Robert G. Rieper
The automorphisms of a graph act naturally on its set of labeled imbeddings to produce its unlabeled imbeddings. The imbedding sum of a graph is a polynomial that contains useful i…
math.CO2000
Continued fractions and Catalan problems
Mahendra Jani, Robert G. Rieper
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…