On the One Property of the Free Components Concerning to the Sum of Equal Powers

• Main Author: Alexander I. Nikonov
• Format: Article
• Language: English
• Published: Samara State Technical University 2014-09-01
• Series: Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
• Subjects: sum of equal powers; free components; number of arrangements; binomial factors
• Online Access: http://mi.mathnet.ru/eng/vsgtu1333

The given paper contains the proof of that the number of combinatorial arrangements coincides with free components of the sums of equal powers with the natural bases and parameters in the presence of the simple equality connecting elements of these arrangements. In the proof the modified exposition of the components participating in formation of the sum of equal powers is used. This exposition becomes simpler and led to an aspect of product of binomial factors. Other variants of construction of corresponding product of binomial factors do not exist here. The received proof allows both to represent number of arrangements in the form of product, and to apply at this representation summation elements. Thus, the number of arrangements supposes characteristic expression not only in the form of product of its elements.