A bijection between ternary trees and a subclass of Motzkin paths

Helmut Prodinger; Sarah J. Selkirk

A bijection between ternary trees and a subclass of Motzkin paths

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arxiv 1808.01907 v2 pith:MMOASN46 submitted 2018-08-06 math.CO

Helmut Prodinger , Sarah J. Selkirk This is my paper · ORCID

classification math.CO

keywords bijectiontreesmotzkinpathssubclassternarygeneralizedgiven

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abstract

A bijection between ternary trees with $n$ nodes and a subclass of Motzkin paths of length $3n$ is given. This bijection can then be generalized to $t$-ary trees.

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Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations
math.CO 2019-08 conditional novelty 6.0 of 10

Nine classes of pattern-avoiding uniquely sorted permutations are enumerated via bijections with Dyck, S-Motzkin, and Schröder paths, confirming Defant's conjectures.

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