ALGEBRAIC COMBINATORICS

Independent Spaces of $q$-Polymatroids
Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 727-744.

This paper is devoted to the study of independent spaces of $q$-polymatroids. With the aid of an auxiliary $q$-matroid it is shown that the collection of independent spaces satisfies the same properties as for $q$-matroids. However, in contrast to $q$-matroids, the rank value of an independent space does not agree with its dimension. Nonetheless, the rank values of the independent spaces fully determine the $q$-polymatroid, and this fact can be exploited to derive a cryptomorphism of $q$-polymatroids. Finally, the notions of minimal spanning spaces, maximally strongly independent spaces, and bases will be elaborated on.

Revised:
Accepted:
Published online:
DOI: 10.5802/alco.241
Classification: 05B35,  05A30
Keywords: $q$-polymatroids, rank-metric codes, independent spaces.
Gluesing-Luerssen, Heide 1; Jany, Benjamin 1

1 University of Kentucky Dept. of Mathematics Lexington, KY 40506 (USA)
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Gluesing-Luerssen, Heide; Jany, Benjamin. Independent Spaces of $q$-Polymatroids. Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 727-744. doi : 10.5802/alco.241. https://alco.centre-mersenne.org/articles/10.5802/alco.241/

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