Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On intersection density of transitive groups of degree a product of two
  odd primes   Two elements $g$ and $h$ of a permutation group $G$ acting on a set $V$ are
said to be intersecting if $g(v) = h(v)$ for some $v \in V$. More generally, a
subset ${\cal F}$ of $G$ is an intersecting set if every pair of elements of
${\cal F}$ is intersecting. The intersection density $\rho(G)$ of a transitive
permutation group $G$ is the maximum value of the quotient $|{\cal F}|/|G_v|$
where $G_v$ is a stabilizer of $v\in V$ and ${\cal F}$ runs over all
intersecting sets in $G$. Intersection densities of transitive groups of degree
$pq$, where $p>q$ are odd primes, is considered. In particular, the conjecture
that the intersection density of every such group is equal to $1$ (posed in [
J.~Combin. Theory, Ser. A 180 (2021), 105390]) is disproved by constructing a
family of imprimitive permutation groups of degree $pq$ (with blocks of size
$q$), where $p=(q^k-1)/(q-1)$, whose intersection density is equal to $q$. The
construction depends heavily on certain equidistant cyclic codes $[p,k]_q$ over
the field $\mathbb{F}_q$ whose codewords have Hamming weight strictly smaller
than $p$.

11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int