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Cyclic k-cycle systems of order 2kn + k: A solution of the last open cases

✍ Scribed by Andrea Vietri

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
144 KB
Volume
12
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

We exhibit cyclic (K~v~, C~k~)‐designs with v > k, v ≡ k (mod 2__k__), for k an odd prime power but not a prime, and for k = 15. Such values were the only ones not to be analyzed yet, under the hypothesis v ≡ k (mod 2__k__). Our construction avails of Rosa sequences and approximates the Hamiltonian case (v = k), which is known to admit no cyclic design with the same values of k. As a particular consequence, we settle the existence question for cyclic (K~v~, C~k~)‐designs with k a prime power. © 2004 Wiley Periodicals, Inc. J Combin Designs 12: 299–310, 2004.

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