Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Even-freeness of cyclic 2-designs   A Steiner 2-design of block size k is an ordered pair (V, B) of finite sets
such that B is a family of k-subsets of V in which each pair of elements of V
appears exactly once. A Steiner 2-design is said to be r-even-free if for every
positive integer i =< r it contains no set of i elements of B in which each
element of V appears exactly even times. We study the even-freeness of a
Steiner 2-design when the cyclic group acts regularly on V. We prove the
existence of infinitely many nontrivial Steiner 2-designs of large block size
which have the cyclic automorphisms and higher even-freeness than the trivial
lower bound but are not the points and lines of projective geometry.

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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph