Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the distances between Latin squares and the smallest defining set
  size   In this note we show that for each Latin square $L$ of order $n\geq 2$, there
exists a Latin square $L'\neq L$ of order $n$ such that $L$ and $L'$ differ in
at most $8\sqrt{n}$ cells. Equivalently, each Latin square of order $n$
contains a Latin trade of size at most $8\sqrt{n}$. We also show that the size
of the smallest defining set in a Latin square is $\Omega(n^{3/2})$. %That is,
there are constants $c$ and $n_0$ such that for any $n>n_0$ the size of the
smallest defining %set of order $n$ is at least $cn^{3/2}$.

26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
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The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga