A note on 2-distant noncrossing partitions and weighted Motzkin paths
- Gessel, Ira M.
- Kim, Jang Soo
Publication date
December 2010
DOI Publisher
Elsevier B.V. Published by Elsevier B.V.Abstract
AbstractWe 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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