On the combinatorics of leftist trees

P. Nogueira
2001 Discrete Applied Mathematics  
Let 'n be the number of leftist trees with n nodes. The corresponding (ordinary) generating function '(x) is shown to satisfy an explicit functional equation, from which a speciÿc recurrence for the 'n is obtained. Some basic analytic properties of '(x) are uncovered. Then the problem of determining average quantities (expected additive weights, in the notation of Kemp (Acta Inform. 26 (1989) 711-740)) related to the distribution of nodes is re-analysed. Finally, the average height of leftist
more » ... ees is shown to be asymptotic to n 1=2 , apart from a multiplicative constant that can be evaluated with high accuracy. ? 2001 Elsevier Science B.V. All rights reserved. MSC: 05C05; 05C30 0166-218X/01/$ -see front matter ? 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 6 -2 1 8 X ( 0 0 ) 0 0 2 5 0 -X
doi:10.1016/s0166-218x(00)00250-x fatcat:zf4ykij4vjbfta42xr4pocayuq