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On trees and noncrossing partitions

✍ Scribed by Martin Klazar

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 426 KB
Volume: 82
Category: Article
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(97)00118-2

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✦ Synopsis

We give a simple and natural proof of (an extension of) the identity P(X. 1. )I ) = t-'2( X I. I -I. II --I ). The number P(li, I, 17) counts noncrossing partitions of { I, 2.

I} unto II parts such that no part contains two numbers .Y and J'. O<.v --.v<k. The lower index 2 indicate\ partitions with no part of size three or more. We USC the identity to give quick proofs of the closed t'ormulac for P(k. I, n) when k is I. 2. or 3.

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