Authors: Šešelja, Branimir
Slivková, Anna
Tepavčević, Andreja 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On geometric posets and partial matroids
Journal: Algebra Universalis
Volume: 81
Issue: 3
Issue Date: 1-Aug-2020
Rank: M22
ISSN: 0002-5240
DOI: 10.1007/s00012-020-00673-7
The aim of this paper is to extend the notions of geometric lattices, semimodularity and matroids in the framework of finite posets and related systems of sets. We define a geometric poset as one which is atomistic and which satisfies particular conditions connecting elements to atoms. Next, by using a suitable partial closure operator and the corresponding partial closure system, we define a partial matroid. We prove that the range of a partial matroid is a geometric poset under inclusion, and conversely, that every finite geometric poset is isomorphic to the range of a particular partial matroid. Finally, by introducing a new generalization of semimodularity from lattices to posets, we prove that a poset is geometric if and only if it is atomistic and semimodular.
Article no. 42
Keywords: Centralized system | Geometric posets | Partial closure operator | Partial closure system | Semimodularity
Publisher: Springer Link
Project: Serbian Ministry of Education, Science and Technological Development through Faculty of Science, University of Novi Sad, (Grant No. 451-03-68/2020-14/200125) and through Mathematical Institute of the Serbian Academy of Sciences and Arts

Show full item record

Page view(s)

checked on Mar 26, 2023

Google ScholarTM




Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.