## Abstract This paper gives a proof of the existence of antiβmitre Steiner triple systems of order __n__ for every __n__ββ‘β1,3 mod 6 except for __n__β=β9. Β© 2005 Wiley Periodicals, Inc. J Combin Designs 14: 229β236, 2006
The resolution of the anti-Pasch conjecture
β Scribed by M. J. Grannell; T. S. Griggs; C. A. Whitehead
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 115 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We prove that, in the framework of ordered geometry, the inner form of the Pasch axiom (**IP**) does not imply its outer form (**OP**). We also show that **OP** can be properly split into **IP** and the weak Pasch axiom (**WP**) (Β© 2010 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
This paper proves the Edge-Orbit Conjecture stated by L. Babai (1981, in "Combinatorics" (H. N. V. Temperley, Ed.), pp. 1-40, Cambridge Univ. Press, London). We say a graph \(X\) represents a group \(G\) if \(\operatorname{Aut}(X) \cong G\). Let \(m_{c}(G)\) be the minimum number of edge orbits amon
Beck and Fiala conjectured in 1981 that for any set system S of maximum degree t on a finite ground set X , a coloring Ο : holds for all S β S, where Ο(S) = xβS Ο(x). We prove a weaker statement, namely that for any fixed p β₯ 1, a coloring Ο exists such that the pth degree average of |Ο(S)| over S
## Abstract We will show the Hodge conjecture and the Tate conjecture are true for the Hilbert schemes of points on an abelian surface or on a Kummer surface. (Β© 2006 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
## Abstract The conjecture that for all sufficiently large __p__ any tournament of order __p__ is uniquely reconstructable from its pointβdeleted subtournaments is shown to be false. Counterexamples are presented for all orders of the form 2^n^ + 1 and 2^n^ + 2. The largest previously known counter