Concerning a certain set of arrangements

@inproceedings{Dushnik1950ConcerningAC,
  title={Concerning a certain set of arrangements},
  author={Ben Dushnik},
  year={1950}
}
there exists an arrangement in S in which ak follows all the a, with i < k. Such sets S surely exist; for example, any set of m arrangements whose terminal elements are 1, 2, , m, respectively, will obviously be k-suitable for any k ? m. The smallest cardinal number N such that there exists a set of N arrangements which is k-suitable for m will be denoted by N(m, k); this is therefore a well defined positive integer for any m and k, k <m. In any collection of arrangements of the first m… 
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