Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 1-Overlap Cycles for Steiner Triple Systems   A number of applications of Steiner triple systems (e.g. disk erasure codes)
exist that require a special ordering of its blocks. Universal cycles,
introduced by Chung, Diaconis, and Graham in 1992, and Gray codes are examples
of listing elements of a combinatorial family in a specific manner, and Godbole
invented the following generalization of these in 2010. 1-overlap cycles
require a set of strings to be ordered so that the last letter of one string is
the first letter of the next. In this paper, we prove the existence of
1-overlap cycles for automorphism free Steiner triple systems of each possible
order. Since Steiner triple systems have the property that each block can be
represented uniquely by a pair of points, these 1-overlap cycles can be
compressed by omitting non-overlap points to produce rank two universal cycles
on such designs, expanding on the results of Dewar.

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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an