Results on Functions on Dedekind Multisets

Abstract

Many real-life problems are well represented only by sets which allow repetition(s), such as the multiset. Although not limited to the following, such cases may arise in a database query, chemical structures and computer programming. The set of roots of a polynomial, say f ( x ) , has been found to correspond to a multiset, say F. If f ( x ) and g ( x ) are polynomials whose sets of roots respectively correspond to the multisets F ( x ) and G ( x ) , the set of roots of their product, f ( x ) g ( x ) , corresponds to the multiset F ⊎ G , which is the sum of multisets F and G. In this paper, some properties of the algebraic sum of multisets ⊎ and some results on selection are established. Also, the count function of the image of any function on Dedekind multisets is defined and some of its properties are established. Some applications of these multisets are also given.

Keywords

• multisets
• functions on multiset
• selection operation
• submultiset