A note on 2-distant noncrossing partitions and weighted Motzkin paths

Details A note on 2-distant noncrossing partitions and weighted Motzkin paths A note on 2-distant noncrossing partitions and weighted Motzkin paths

2010-03-27

arxiv.org/abs/1003.5301v2

Discrete Math., (310) 3421-3425, 2010

Mathematics

Combinatorics

6 pages, 2 figures

Scientific paper

We prove a conjecture of Drake and Kim: the number of $2$-distant noncrossing
partitions of $\{1,2,...,n\}$ is equal to the sum of weights of Motzkin paths
of length $n$, where the weight of a Motzkin path is a product of certain
fractions involving Fibonacci numbers. We provide two proofs of their
conjecture: one uses continued fractions and the other is combinatorial.

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