Report
The Cyclic Flats of a $q$-Matroid
| العنوان: | The Cyclic Flats of a $q$-Matroid |
|---|---|
| المؤلفون: | Alfarano, Gianira N., Byrne, Eimear |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Computer Science - Information Theory |
| الوصف: | In this paper we develop the theory of cyclic flats of $q$-matroids. We show that the lattice of cyclic flats, together with their ranks, uniquely determines a $q$-matroid and hence derive a new $q$-cryptomorphism. We introduce the notion of $\mathbb{F}_{q^m}$-independence of an $\mathbb{F}_q$-subspace of $\mathbb{F}_q^n$ and we show that $q$-matroids generalize this concept, in the same way that matroids generalize the notion of linear independence of vectors over a given field. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2204.02353 |
| رقم الانضمام: | edsarx.2204.02353 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |