Real phase structures on matroid fans and ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
Real phase structures on matroid fans and matroid orientations
Author(s) :
Rau, Johannes [Auteur]
Universidad de los Andes [Bogota] [UNIANDES]
Renaudineau, Arthur [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Shaw, Kris [Auteur]
University of Oslo [UiO]
Universidad de los Andes [Bogota] [UNIANDES]
Renaudineau, Arthur [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Shaw, Kris [Auteur]
University of Oslo [UiO]
Journal title :
Journal of the London Mathematical Society
Pages :
3687-3710
Publisher :
London Mathematical Society ; Wiley
Publication date :
2022-09
ISSN :
0024-6107
HAL domain(s) :
Mathématiques [math]/Mathématiques générales [math.GM]
English abstract : [en]
We introduce the notion of real phase structure on rational polyhedral fans in Euclidean space. Such a structure consists of an assignment of affine spaces over to each top-dimensional face of the fan subject to two ...
Show more >We introduce the notion of real phase structure on rational polyhedral fans in Euclidean space. Such a structure consists of an assignment of affine spaces over to each top-dimensional face of the fan subject to two conditions. Given an oriented matroid we can construct a real phase structure on the fan of the underlying matroid. Conversely, we show that from a real phase structure on a matroid fan we can produce an orientation of the underlying matroid. Thus real phase structures are cryptomorphic to matroid orientations. The topes of the orientated matroid are recovered immediately from the real phase structure. We also provide a direct way to recover the signed circuits of the oriented matroid from the real phase structure.Show less >
Show more >We introduce the notion of real phase structure on rational polyhedral fans in Euclidean space. Such a structure consists of an assignment of affine spaces over to each top-dimensional face of the fan subject to two conditions. Given an oriented matroid we can construct a real phase structure on the fan of the underlying matroid. Conversely, we show that from a real phase structure on a matroid fan we can produce an orientation of the underlying matroid. Thus real phase structures are cryptomorphic to matroid orientations. The topes of the orientated matroid are recovered immediately from the real phase structure. We also provide a direct way to recover the signed circuits of the oriented matroid from the real phase structure.Show less >
Language :
Anglais
Popular science :
Non
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