A note on 2-distant noncrossing partitions and weighted Motzkin paths |
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| Authors: | Ira M. Gessel |
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| Affiliation: | Department of Mathematics, MS 050, Brandeis University, Waltham, MA 02454-9110, USA LIAFA, Université Paris Diderot, 175 rue du Chevaleret, 75013 Paris, France |
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| 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. |
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| Keywords: | Continued fraction Fibonacci number Motzkin path Dyck path Schrö der path |
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