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

作者：Gessel Ira M; Kim Jang Soo^*

来源：Discrete Mathematics, 2010, 310(23): 3421-3425.

DOI：10.1016/j.disc.2010.07.017

• Continued fraction
• Fibonacci number
• Motzkin path
• Dyck path
• Schroder path

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.

• 出版日期2010-12-6