EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 95[109], pp. 111–117 (2014)

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Silvia Ghilezan, Jovanka Pantovic, Gradimir Vojvodic

Faculty of Technical Sciences, University of Novi Sad, Serbia; Faculty of Science, University of Novi Sad, Serbia

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: multiset, bag

Classification (MSC2000): 08A99; 03C99

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Electronic fulltext finalized on: 31 Mar 2014. This page was last modified: 2 Apr 2014.

© 2014 Mathematical Institute of the Serbian Academy of Science and Arts
© 2014 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition