How many cubes are orientable? | Vidéo | Carmin.tv

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How many cubes are orientable?

By Ilda P. F. Da Silva

Appears in collection : Combinatorial geometries: matroids, oriented matroids and applications / Géométries combinatoires : matroïdes, matroïdes orientés et applications

A cube is a matroid over $C^n={-1,+1}^n$ that contains as circuits the usual rectangles of the real affine cube packed in such a way that the usual facets and skew-facets are hyperplanes of the matroid. How many cubes are orientable? So far, only one: the oriented real affine cube. We review the results obtained so far concerning this question. They follow two directions: 1)Identification of general obstructions to orientability in this class. (da Silva, EJC 30 (8), 2009, 1825-1832). 2)(work in collaboration with E. Gioan) Identification of algebraic and geometric properties of recursive families of non-negative integer vectors defining hyperplanes of the real affine cube and the analysis of this question and of las Vergnas cube conjecture in small dimensions.

Information about the video

Date of recording 24/09/2018
Date of publication 01/10/2018
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19450403
Cite this video Da Silva, Ilda P. F. (24/09/2018). How many cubes are orientable?. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19450403
URL https://dx.doi.org/10.24350/CIRM.V.19450403

Domain(s)

Bibliography

da Silva, I.P.F. (2005). Recursivity and geometry of the hypercube. Linear Algebra and its Applications, 397, 223-233 - https://doi.org/10.1016/j.laa.2004.10.016
da Silva, I.P.F. (2008). Cubes and orientability. Discrete Mathematics, 308(16), 3574-3585 - https://doi.org/10.1016/j.disc.2007.07.043
da Silva, I.P.F. (2009). On minimal non-orientable matroids with $2n$ elements and rank $n$. European Journal of Combinatorics, 30(8), 1825-1832 - https://doi.org/10.1016/j.ejc.2008.12.003
da Silva, I.P.F., & Gioan, I. (2018). Rectangles and hyperplanes of the hypercube. Working paper -

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