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Higher Bruhat orders of types B and C

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Abstract

We propose versions of higher Bruhat orders for types B and C. This is based on a theory of higher Bruhat orders of type A and their geometric interpretations (due to Manin–Shekhtman, Voevodskii–Kapranov, and Ziegler), and on our study of the so-called symmetric cubillages of cyclic zonotopes.

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Notes

  1. Our definition here is slightly different from the standard definition of a digraph morphism; to get a complete correspondence, we should add “loops” (edges connecting identical vertices).

  2. This resembles, though slightly differs from, the concept of full functors in category theory.

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Authors and Affiliations

  1. Central Institute of Economics and Mathematics of the RAS, 47, Nakhimovskii Prospect, 117418, Moscow, Russia

    Vladimir I. Danilov & Alexander V. Karzanov

  2. Institute for Information Transmission Problems of the RAS, 19, Bol’shoi Karetnyi per, 127051, Moscow, Russia

    Gleb A. Koshevoy

  3. HSE University, Moscow, Russia

    Gleb A. Koshevoy

Authors
  1. Vladimir I. Danilov
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  2. Alexander V. Karzanov
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  3. Gleb A. Koshevoy
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Correspondence to Alexander V. Karzanov.

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Gleb A. Koshevoy: Supported in part by Grant 22-41-02028 from the Russian Science Foundation.

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Danilov, V.I., Karzanov, A.V. & Koshevoy, G.A. Higher Bruhat orders of types B and C. J Algebr Comb (2024). https://doi.org/10.1007/s10801-024-01334-x

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