Autor(en): | Hoya, Marcel |
Titel: | Universal partial hyperfields of matroids and their prespaces of orderings |
Sprache (ISO): | en |
Zusammenfassung: | We associate a partial hyperfield šā½ā°ā¾(M) with every matroid M by defining an addition on the elements of its inner Tutte group with an additional zero element such that M is representable over šā½ā°ā¾(M), and every representation of M over a partial hyperfield F factors over the representation of M over šā½ā°ā¾(M). We investigate the relationship between šā½ā°ā¾(M) and šā½ā°ā¾(N) for minors N of M and prove that šā½ā°ā¾(M) is the coproduct of šā½ā°ā¾(Mįµ¢), i=1,ā¦,k where Mā,ā¦,Mā are the connected components of M. Further, we examine the possible non-trivial decompositions of šā½ā°ā¾(M) as a coproduct and present sufficient geometrical conditions under which no such decomposition exists. We develop an Artin-Schreier-Theory for partial hyperfields and show that the orderings of a partial hyperfield form a prespace of orderings, which is in general not a space of orderings in the sense of Marshall, even for the partial hyperfield šā½ā°ā¾(M) of a matroid M. Moreover, we provide examples of matroids M for which šā½ā°ā¾(M) is a hyperfield and its prespace of orderings is a space of orderings in the sense of Marshall, including affine space of dimension at least 3 and affine translation planes whose kernel contains at least four elements, for which the inner Tutte group was not known before. |
Schlagwƶrter: | Partial hyperfields Inner Tutte group Matroids Combinatorial geometries Affine planes Affine spaces Projective planes Projective spaces |
Schlagwƶrter (RSWK): | Orientiertes Matroid Kombinatorische Geometrie Kƶrpertheorie |
URI: | http://hdl.handle.net/2003/42414 http://dx.doi.org/10.17877/DE290R-24250 |
Erscheinungsdatum: | 2023 |
Enthalten in den Sammlungen: | Lehrstuhl VI Algebra und Geometrie |
Dateien zu dieser Ressource:
Datei | Beschreibung | GrƶĆe | Format | |
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Dissertation_Hoya.pdf | DNB | 1.53 MB | Adobe PDF | Ćffnen/Anzeigen |
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