COMBINATORIAL ANALYSIS IN THE SCHEME OF ALLOCATION OF DISTINGUISHABLE PARTICLES INTO INDISTINGUISHABLE CELLS WITH A GIVEN NUMBER OF NON-EMPTY CELLS

Abstract

The scheme of allocating r distinguishable particles into n indistinguishable cells with k non-empty cells is studied along the directions of enumerative combinatorics. They are the direct enumeration of the outcomes of the scheme with a particulardiscipline of their numbering, finding their numbers, establishing a one-to-one correspondence of the types of outcomes with their numbers, also known as numbering problem in direct and inverse statements, and modeling of outcomes of the scheme.

Keywords

• minimum numbers of particles on cells
• portion additions.