Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal sizes of subspace partitions   A subspace partition $\Pi$ of $V=V(n,q)$ is a collection of subspaces of $V$
such that each 1-dimensional subspace of $V$ is in exactly one subspace of
$\Pi$. The size of $\Pi$ is the number of its subspaces. Let $\sigma_q(n,t)$
denote the minimum size of a subspace partition of $V$ in which the largest
subspace has dimension $t$, and let $\rho_q(n,t)$ denote the maximum size of a
subspace partition of $V$ in which the smallest subspace has dimension $t$. In
this paper, we determine the values of $\sigma_q(n,t)$ and $\rho_q(n,t)$ for
all positive integers $n$ and $t$. Furthermore, we prove that if $n\geq 2t$,
then the minimum size of a maximal partial $t$-spread in $V(n+t-1,q)$ is
$\sigma_q(n,t)$.

31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an