Felipe Rincón - Isotropical Linear Spaces and Valuated Delta-Matroids

dmtcs:2954 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2954
Isotropical Linear Spaces and Valuated Delta-Matroids

Authors: Felipe Rincón

    The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of an $n \times n$ skew-symmetric matrix. Its points correspond to $n$-dimensional isotropic subspaces of a $2n$-dimensional vector space. In this paper we tropicalize this picture, and we develop a combinatorial theory of tropical Wick vectors and tropical linear spaces that are tropically isotropic. We characterize tropical Wick vectors in terms of subdivisions of Delta-matroid polytopes, and we examine to what extent the Wick relations form a tropical basis. Our theory generalizes several results for tropical linear spaces and valuated matroids to the class of Coxeter matroids of type $D$.


    Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
    Section: Proceedings
    Published on: January 1, 2011
    Imported on: January 31, 2017
    Keywords: spinor variety,isotropic subspace,tropical linear space,valuated matroid,delta-matroid,matroid subdivision,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
    Fundings :
      Source : OpenAIRE Research Graph
    • FRG: Collaborative Research: Semidefinite optimization and convex algebraic geometry; Funder: National Science Foundation; Code: 0757207
    • Computational Algebraic Geometry; Funder: National Science Foundation; Code: 0456960

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    Source : ScholeXplorer IsReferencedBy ARXIV 1809.03350
    Source : ScholeXplorer IsReferencedBy DOI 10.1007/s10801-019-00916-4
    Source : ScholeXplorer IsReferencedBy DOI 10.48550/arxiv.1809.03350
    • 10.48550/arxiv.1809.03350
    • 10.1007/s10801-019-00916-4
    • 10.1007/s10801-019-00916-4
    • 10.1007/s10801-019-00916-4
    • 1809.03350
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