Enumeration of small nonisomorphic 1-rotational twofold triple systems
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 hav...
Saved in:
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2011
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/91832 http://hdl.handle.net/10220/6940 http://www.jstor.org/stable/2153077 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
|---|