Séminaire Lotharingien de Combinatoire, 84B.60 (2020), 12 pp.

Jean-Philippe Labbé

Universal oriented Matroids for Subword Complexes of Coxeter Groups

Abstract. We study geometric realizations of subword complexes using multilinear algebra and combinatorics on reduced words. Namely, we provide an explicit description of partial oriented matroids using parameter tensors that encapsulate the necessary information to obtain geometric realizations of subword complexes, and show that every geometric realization is parametrized by a certain parameter tensor.


Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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