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Flag matroids : algebra and geometry

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2018

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Cameron, Amanda
Seynnaeve, Tim

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http://arxiv.org/abs/1811.00272

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Zusammenfassung

Matroids are ubiquitous in modern combinatorics. As discovered by Gelfand, Goresky, MacPherson and Serganova there is a beautiful connection between matroid theory and the geometry of Grassmannians: realizable matroids correspond to torus orbits in Grassmannians. Further, as observed by Fink and Speyer general matroids correspond to classes in the K-theory of Grassmannians. This yields in particular a geometric description of the Tutte polynomial. In this review we describe all these constructions in detail, and moreover we generalise some of them to polymatroids. More precisely, we study the class of flag matroids and their relations to flag varieties. In this way, we obtain an analogue of the Tutte polynomial for flag matroids.

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510 Mathematik

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ISO 690CAMERON, Amanda, Rodica DINU, Mateusz MICHALEK, Tim SEYNNAEVE, 2018. Flag matroids : algebra and geometry
BibTex
@unpublished{Cameron2018matro-55481,
  year={2018},
  title={Flag matroids : algebra and geometry},
  author={Cameron, Amanda and Dinu, Rodica and Michalek, Mateusz and Seynnaeve, Tim}
}
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