A note on 2-distant noncrossing partitions and weighted Motzkin paths
نویسندگان
چکیده
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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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 310 شماره
صفحات -
تاریخ انتشار 2010