Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Sidon-type condition on set systems   Consider families of $k$-subsets (or blocks) on a ground set of size $v$.
Recall that if all $t$-subsets occur with the same frequency $\lambda$, one
obtains a $t$-design with index $\lambda$. On the other hand, if all
$t$-subsets occur with different frequencies, such a family has been called (by
Sarvate and others) a $t$-adesign. An elementary observation shows that such
families always exist for $v > k \ge t$. Here, we study the smallest possible
maximum frequency $\mu=\mu(t,k,v)$.
  The exact value of $\mu$ is noted for $t=1$ and an upper bound (best possible
up to a constant multiple) is obtained for $t=2$ using PBD closure. Weaker, yet
still reasonable asymptotic bounds on $\mu$ for higher $t$ follow from a
probabilistic argument. Some connections are made with the famous Sidon problem
of additive number theory.

30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
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The categories of this paper are: solv-int