Linearly dependent vectorial decomposition of clutters
This paper deals with the question of completing a monotone increasing family of subsets of a finite set to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we demonstrate that such vectorial completions of the family of subsets ¿ exist and, in addition,...
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| Format: | article |
| Publication Date: | 2014 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/27361 |
| Online Access: | https://hdl.handle.net/2117/27361 https://dx.doi.org/10.1016/j.endm.2014.08.028 |
| Access Level: | Open access |
| Keyword: | Clutter Antichain Hypergraph Matroid Decomposition. Classificació AMS::05 Combinatorics Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Summary: | This paper deals with the question of completing a monotone increasing family of subsets of a finite set to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we demonstrate that such vectorial completions of the family of subsets ¿ exist and, in addition, we show that the minimal vectorial completions of the family ¿ provide a decomposition of the clutter of the inclusion-minimal elements of ¿. The computation of such vectorial decomposition of clutters is also discussed in some cases. |
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