A leaf of a plane tree is called an old leaf if it is the leftmost child of its parent, and it is called a young leaf otherwise. In this paper we enumerate plane trees with a given number of old leaves and young leaves. The formula is obtained combinatorially by presenting two bijections between plane trees and 2-Motzkin paths which map young leaves to red horizontal steps, and old leaves to up...

The reproductive potential of a Meloidogyne javanica population on 64 commercial corn hybrids and 33 corn inbred lines was determined in greenhouse experiments. Reproduction was measured by determining RF values (final egg number per initial egg number) and number of eggs per gram of fresh root. All corn hybrids supported reproduction greater than RF = 1.0. RF values for the hybrids ranged from...

The problem of counting plane trees with n edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Stanley. This identity was also obtained by Bonin, Shapiro and Simion in their study of Schröder paths, and it was recently derived by Coker using the Lagrange inversion formula. An equivalent problem for partitions of set...

The study was conducted to compare between nine cottonseeds genotypes (Gossipum hirsutum L) which included, two locale Iraqi Coker 310 and Lachata are three of the Bakhtegan, Khordad, Varamin from Iran, four them Cafko, Dunn 1047, Montana, Stoneville America (USA) on fiber quality. field experiment designed with randomised complete block design using replicates in Grdmal village, south Erbil, i...

Objectives: Background: Revision ACL reconstruction (ACLR) has demonstrated worse functional outcomes and higher reinjury rates in young patients. Psychological associations with revision surgery have not previously been evaluated. Purpose: To investigate levels of psychological readiness stress patients after ACLR Methods: Patients, ages 10-35, were enrolled who underwent at one center by six ...