<abstract xmlns="http://www.w3.org/1999/xhtml">This paper is inspired by a text of the book [7] (“úvod do algebry” in Czech, “Introduction to Algebra” in English) of the authors Ladislav Kosmák and Radovan Potůček. They followed the great work of Professor Otakar Borůvka in the field of the partition theory, groupoids and groups and gave them in the context to contemporary modern algebra. Academian Boruvka have deduced and proved many results concerning the partition theory in his publications.His first works [1] and [2] were published during World War II and his monographs [3] and [4] were released in the post-war years.In this paper we deal with a construction of the smallest common coarser of two set partitions associated with equivalence relations, we give a special relation used in the construction and an illustration of blocks of this coarser.</abstract>

This paper is inspired by a text of the book [7] (“úvod do algebry” in Czech, “Introduction to Algebra” in English) of the authors Ladislav Kosmák and Radovan Potůček. They followed the great work of Professor Otakar Borůvka in the field of the partition theory, groupoids and groups and gave them in the context to contemporary modern algebra. Academian Boruvka have deduced and proved many results concerning the partition theory in his publications.His first works [1] and [2] were published during World War II and his monographs [3] and [4] were released in the post-war years.In this paper we deal with a construction of the smallest common coarser of two set partitions associated with equivalence relations, we give a special relation used in the construction and an illustration of blocks of this coarser.

Construction of the Smallest Common Coarser of Two and Three Set Partitions

Faculty of Military Technology, University of Defence, Kounicova 65, 662 10 Brno, Czech Republic

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Construction of the Smallest Common Coarser of Two and Three Set Partitions"}

This paper is inspired by a text of the book [7] (“úvod do algebry” in Czech, “Introduction to Algebra” in English) of the authors Ladislav Kosmák and Radovan...

Construction of the Smallest Common Coarser of Two and Three Set Partitions

Published Online: Dec 10, 2014

Page range: 237 - 246

Received: May 01, 2013

Accepted: Oct 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0019

Keywords
Partition of a set, equivalence relation, smallest common coarser

© 2014 Radovan Potůček

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Construction of the Smallest Common Coarser of Two and Three Set Partitions

Published Online: Dec 10, 2014

Page range: 237 - 246

Received: May 01, 2013

Accepted: Oct 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0019

KeywordsPartition of a set, equivalence relation, smallest common coarser

© 2014 Radovan Potůček

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Partition of a set, equivalence relation, smallest common coarser