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Title:
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Enumeration of small nonisomorphic 1-rotational twofold triple systems.
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Author:
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Chee, Yeow Meng.; Royle, Gordon F.
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Copyright year:
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1992 |
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Abstract:
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In this paper, twofold triple systems of order v are enumerated for all v ≤ 19.
The existence of TS(v , 2)'s (all terms are defined in §2) is completely settled;
the condition v -0 or 1 (mod 3) is known to be both necessary and sufficient
[4]. On the other hand, enumeration efforts have not enjoyed such success. In
fact, the exact number of painvise nonisomorphic TS(v, 2)'s, denoted N(v) ,
has been determined only for v 5 10. In particular, we have N(3) = N(4) = 1
(trivial), N(6) = 1 [5], N(7) = 4 [13], N(9) = 36 [12, 81, and N(10) = 960
[l, 31. One reason for the unavailability of such enumeration results for higher
values of v is the inherent computational complexity of the problem that leads
to a combinatorial explosion effect. To curb this combinatorial explosion, extra
conditions are often imposed to enumerate interesting classes of designs. One
such condition involves specifying automorphisms that the desired designs must
possess. |
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Subject:
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DRNTU::Science::Mathematics::Applied mathematics. |
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Type:
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Journal Article |
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Series/ Journal Title:
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Mathematics of computation. |
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School:
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School of Physical and Mathematical Sciences |
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Rights:
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© 1992 American Mathematical Society. This paper was published in Mathematics of Computation and is made available as an electronic reprint (preprint) with permission of American Mathematical Society. The paper can be found at the following official URL: http://www.jstor.org/stable/2153077. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. |
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Version:
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Published version |
