| Autor: |
Gluesing-Luerssen, Heide, Jany, Benjamin |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We study the direct sum of q-matroids by way of their cyclic flats. Using that the rank function of a q-matroid is fully determined by the cyclic flats and their ranks, we show that the cyclic flats of the direct sum of two q-matroids are exactly all the direct sums of the cyclic flats of the two summands. This simplifies the rank function of the direct sum significantly. A q-matroid is called irreducible if it cannot be written as a (non-trivial) direct sum. We provide a characterization of irreducibility in terms of the cyclic flats and show that every q-matroid can be decomposed into a direct sum of irreducible q-matroids, which are unique up to equivalence. |
| Databáze: |
arXiv |
| Externí odkaz: |
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