Describing the symmetry of one-dimensional figures by power sums of point coordinates

The article examines the problem of describing the symmetry of a one-dimensional figure by power sums of the coordinates of its points. In case ofn points of unit mass, the figure symmetry requires (n+1)/2] values of odd power sums; in case of massive points,n values are required in general. A one-to-one correspondence is established between the coordinates ofn points of the figure and the values of power sums to order (2n−1) inclusive. Translated from Prikladnaya Matematika i Informatika, No. 2, pp. 106–115, 1999.