Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new relationship between block designs   We propose a procedure of constructing new block designs starting from a
given one by looking at the intersections of its blocks with various sets and
grouping those sets according to the structure of the intersections.
  We introduce a symmetric relationship of friendship between block designs
built on a set $V$ and consider families of block designs where all designs are
friends of each other, the so-called friendly families. We show that a friendly
family admits a partial ordering. Furthermore, we exhibit a map from the power
set of $V$, partially ordered by inclusion, to a friendly family of a
particular type which preserves the partial order.

35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga