Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on the Expected Length of the Longest Common Subsequences of two
  i.i.d. Random Permutations   We address a question and a conjecture on the expected length of the longest
common subsequences of two i.i.d.$\ $random permutations of
$[n]:=\{1,2,...,n\}$. The question is resolved by showing that the minimal
expectation is not attained in the uniform case. The conjecture asserts that
$\sqrt{n}$ is a lower bound on this expectation, but we only obtain
$\sqrt[3]{n}$ for it.

13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin