On trees and noncrossing partitions

Martin Klazar
1998 Discrete Applied Mathematics  
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. c 1998 Elsevier Science H.V All right.+ reserved. A'~,.IYIv~~/.\:
more » ... oncrossing partition; Enumeration; Tree: Rijectlon ' Supported by Grants GAUK 194 and G.\t?R 0194 Olh6-2lXX~9X/Sl9.00 C3 1998 Elsevier Science B.V. All rights rcscrvcd PI/ s0166-21xx(97)00118-2
doi:10.1016/s0166-218x(97)00118-2 fatcat:jr7ct5tqqjbkpkhj75z6x35tqm