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Open AccessArticle

Results on Functions on Dedekind Multisets

1
Department of Mathematics and Physics, University of Defence Brno, Kounicova 65, 66210 Brno, Czech Republic
2
Department of Mathematics, Faculty of Science, University of Ibadan, Ibadan 200284, Oyo State, Nigeria
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(9), 1125; https://doi.org/10.3390/sym11091125
Received: 16 July 2019 / Revised: 27 August 2019 / Accepted: 2 September 2019 / Published: 4 September 2019
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. View Full-Text
Keywords: multisets; functions on multiset; selection operation; submultiset multisets; functions on multiset; selection operation; submultiset
MDPI and ACS Style

Hošková-Mayerová, Š.; Onasanya, B.O. Results on Functions on Dedekind Multisets. Symmetry 2019, 11, 1125.

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