Authors: Ghilezan, Silvia 
Pantović, Jovanka
Vojvodić, Gradimir
Title: Binary relations and algebras on multisets
Journal: Publications de l'Institut Mathematique
Volume: 95
Issue: 109
First page: 111
Last page: 117
Issue Date: 1-Jan-2014
Rank: M23
ISSN: 0350-1302
DOI: 10.2298/PIM1409111G
Abstract: 
Contrary to the notion of a set or a tuple, a multiset is an unordered collection of elements which do not need to be different. As multisets are already widely used in combinatorics and computer science, the aim of this paper is to get on track to algebraic multiset theory. We consider generalizations of known results that hold for equivalence and order relations on sets and get several properties that are specific to multisets. Furthermore, we exemplify the novelty that brings this concept by showing that multisets are suitable to represent partial orders. Finally, after introducing the notion of an algebra on multisets, we prove that two algebras on multisets, whose root algebras are isomorphic, are in general not isomorphic.
Keywords: Bag | Multiset
Publisher: Mathematical Institute of the SASA
Project: Representations of logical structures and formal languages and their application in computing 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 

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