Counting subspaces of a finite vector space — 1
✍ Scribed by Amritanshu Prasad
- Book ID
- 107589895
- Publisher
- Indian Academy of Sciences
- Year
- 2010
- Tongue
- English
- Weight
- 274 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0971-8044
No coin nor oath required. For personal study only.
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## Abstract Let __V__~n~(q) denote a vector space of dimension __n__ over the field with __q__ elements. A set ${\cal P}$ of subspaces of __V__~n~(q) is a __partition__ of __V__~n~(q) if every nonzero element of __V__~n~(q) is contained in exactly one element of ${\cal P}$. Suppose there exists a p
If F is the finite field of characteristic p and order q s p , let F F q be the q category whose objects are functors from finite dimensional F -vector spaces to q F -vector spaces, and with morphisms the natural transformations between such q functors. Ž . A fundamental object in F F q is the injec