Title of article
A note on 2-distant noncrossing partitions and weighted Motzkin paths
Author/Authors
Gessel، نويسنده , , Ira M. and Kim، نويسنده , , Jang Soo، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2010
Pages
5
From page
3421
To page
3425
Abstract
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.
Keywords
Continued fraction , Fibonacci number , Schrِder path , Dyck path , Motzkin path
Journal title
Discrete Mathematics
Serial Year
2010
Journal title
Discrete Mathematics
Record number
1599514
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