A composition of n is an ordered collection of one or more positive integers whose sum is n. The number of summands is called the number of parts of the composition. A palindromic composition or palindrome is a composition in which the summands are the same in the given or in reverse order. Compositions may be viewed as tilings of 1-by-n rectangles with 1-by-i rectangles, 1 i n ≤ ≤ . We count t...

A composition of a positive integer n consists of an ordered sequence of positive integers whose sum is n. We investigate compositions in which the summand 2 is not allowed, and count the total number of such compositions and the number of occurrences of the summand i in all such compositions. Furthermore, we explore patterns in the values for Cj(n, 2̂), the number of compositions of n without 2...

specific features of the structure of the ground litter invertebrate community in forest belt ecosystems in the ukrainian steppe zone have been considered. for 14 years invertebrate fauna of the litter of 176 forest belt sites with different composition has been studied with the aid of soil traps. the main characteristics of litter invertebrate communities (total population, a number of species...

abstract: the significance of financial performance of companies makes factors affecting it significant. as a mixed-method research, this paper aimed at investigating the effect of human resources composition in of an organization and the management stability on the financial performance of the organization. first, based on the grounded theory, the indices of human resources composition were id...

A composition σ = a1a2 . . . am of n is an ordered collection of positive integers whose sum is n. An element ai in σ is a strong (weak) record if ai > aj (ai ≥ aj) for all j = 1, 2, . . . , i− 1. Furthermore, the position of this record is i. We derive generating functions for the total number of strong (weak) records in all compositions of n, as well as for the sum of the positions of the rec...

the aim of this study was to evaluate the effect of long-term reduced tillage on yield and weeds of spring barley. treatments consisted of three tillage systems including: (a) conventional tillage (ct), (b) reduced tillage (rt), and (c) herbicide tillage (ht) as the main plot, and two cultivars of spring barley (tocada and rastik) as subplots. the results showed that the yield of both cultivars...

We prove a simple relationship between extended binomial coefficients — natural extensions of the well-known binomial coefficients — and weighted restricted integer compositions. Moreover, we give a very useful interpretation of extended binomial coefficients as representing distributions of sums of independent discrete random variables. We apply our results, e.g., to determine the distribution...