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A note on 2-distant noncrossing partitions and weighted Motzkin paths
- Source :
- Discrete Math., (310) 3421-3425, 2010
- Publication Year :
- 2010
-
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.<br />Comment: 6 pages, 2 figures
- Subjects :
- Mathematics - Combinatorics
05A15, 05A19
Subjects
Details
- Database :
- arXiv
- Journal :
- Discrete Math., (310) 3421-3425, 2010
- Publication Type :
- Report
- Accession number :
- edsarx.1003.5301
- Document Type :
- Working Paper