Abstract
Positroids are a class of matroids in bijection with several combinatorial objects. In particular, every positroid can be constructed from a decorated permutation or from a Le-graph.
In this paper, we present two algorithms, one that computes the rank of a subset of a positroid using its representation as a Le-graph and the other takes as input a decorated permutation \(\sigma \) and outputs the Le-graph that represent the same positroid as \(\sigma \). These two algorithms combined form an improvement to Mcalmon and Oh’s result on the computation of the rank function of a positroid from the decorated permutation.
This work was carried out during a visit of Guzmán-Pro at FernUniversität in Hagen, supported by DAAD grant 57552339.
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Chidiac, L., Guzmán-Pro, S., Hochstättler, W., Youssef, A. (2023). An Efficient Computation of the Rank Function of a Positroid. In: Fernau, H., Jansen, K. (eds) Fundamentals of Computation Theory. FCT 2023. Lecture Notes in Computer Science, vol 14292. Springer, Cham. https://doi.org/10.1007/978-3-031-43587-4_11
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DOI: https://doi.org/10.1007/978-3-031-43587-4_11
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