ABOUT FACES OF THE GENERAL PERMUTABLE POLYHEDRON - IemetsО. О.; Yemets` O. O.; PolyakovІ. М. (Computer Science and Applied Mathematics, 2016)
New facts for the faces of arbitrary dimension of general permutation polyhedron are considered in the article. Herewith the general permutation polyhedron is set as the convex hull of the multiset of elements, each of which has its own multiplicity. Two forms of general permutation polyhedron are considered: the so-called direct form, in which the elements of the multiset are numbered (are ordered) by not ascending order and the symmetrical to it form with the opposite numbered elements. The system of required sets of indices and their characteristics are built on the basis of the m-faces criterion of general permutation polyhedron in the direct form. They allow getting a new criterion of mfaces of general permutation polyhedron in a symmetrical form. Two equivalent forms for the symmetrical form are offered. They are suitable for the use in different cases.