Séminaire lotharingien de combinatoire, Tome 47 (2001-2002)
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Andreas Dress; M. Klucznik; Jack Koolen; Vincent Moulton. 2kn - Binomial(2k+1,2). Séminaire lotharingien de combinatoire, Tome 47 (2001-2002). http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a1/
@article{SLC_2001-2002_47_a1,
author = {Andreas Dress and M. Klucznik and Jack Koolen and Vincent Moulton},
title = {2kn - {Binomial(2k+1,2)}},
journal = {S\'eminaire lotharingien de combinatoire},
year = {2001-2002},
volume = {47},
url = {http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a1/}
}
TY - JOUR
AU - Andreas Dress
AU - M. Klucznik
AU - Jack Koolen
AU - Vincent Moulton
TI - 2kn - Binomial(2k+1,2)
JO - Séminaire lotharingien de combinatoire
PY - 2001-2002
VL - 47
UR - http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a1/
ID - SLC_2001-2002_47_a1
ER -
%0 Journal Article
%A Andreas Dress
%A M. Klucznik
%A Jack Koolen
%A Vincent Moulton
%T 2kn - Binomial(2k+1,2)
%J Séminaire lotharingien de combinatoire
%D 2001-2002
%V 47
%U http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a1/
%F SLC_2001-2002_47_a1
It is shown that every cyclic split system S defined on an n-set with #S > 2kn - Binomial(2k+1, 2) for some k = (n-1)/2 always contains a subset of k+1 pairwise incompatible splits provided one has min(k,n - (2k+1)) = 3. In addition, some related old and new conjectures are also discussed.
