|Table of Contents|

Simple Kirkman Frames With Index 2 and 3(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2008年01期
Page:
15-20
Research Field:
数学
Publishing date:

Info

Title:
Simple Kirkman Frames With Index 2 and 3
Author(s):
Cao Haitao; Wu Yan
Institute of Mathematics,School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China
Keywords:
s imp le;  fram e d es ign;  group-d ivisib le d es ign
PACS:
O157.2
DOI:
-
Abstract:
A (K, λ)-fram e is a GDD ( X, G, B) in wh ich the co llection o f b lo cksB can be pa rtitioned into ho ley para lle l c lasses, each ho ley paralle l c lass be ing a pa rtition of G \Gj for som e Gj ∈ G. A fram e is called s imp le if a ll its b locks are distinc t. S imp le fram es are powe rfu l fo r the construc tion of sim ple K irkm an packing designs, w hich can be used in the construction of un iform designs in statistics. In this paper, we sha ll prove that the necessary conditions for simp le K irkm an fram es of type tu w ith index 2 and 3 are a lso sufficient

References:

[ 1] Fang K, Ge G, LiuM, et a.l Com binato rial constructions for optim a l supersa turated designs[ J]. D iscre teM a th, 2004, 279 ( 1 /3): 191-202.
[ 2] Fang K, Lu X, Tang Y, et a.l Constructions o f un iform designs by us ing reso lv ab le packings and cover ing s[ J]. D iscrete M ath, 2004, 274( 1 /3) : 25-40.
[ 3] Stinson D R. Frames fo rK irkm an tr ip le system s[ J]. D iscre teM ath, 1987, 65( 3): 289-300.
[ 4] Shen H. Reso lvable two- fo ld trip le system s w ithout repeated b locks[ J]. Sc ience Bulle tin, 1988, 33: 1 855-1 857.
[ 5] Fur ino S F, M iao Y, Y in J X. Fram es and Resolvable Des igns: Uses, Constructions and Ex istence[M ]. BocaRa ton: CRC Press, 1996.
[ 6] Brouwe rA E. Optim al pack ing s ofK 4 s into aK n [ J]. J Com bin Theo ry SerA, 1979, 26( 3): 278-297.
[ 7] Brouwe rA E, H ananiH, Schrijver A. G roup div is ible designs w ith b lock-size four[ J]. D iscreteM a th, 1977, 20: 1-10.
[ 8] Co lbourn C J, D initz J H. CRC H andbook of Com binato rial Designs[M ]. Boca Raton: CRC Press, 1996.

Memo

Memo:
-
Last Update: 2013-05-05