TY - JOUR
T1 - Kirkman frames having hole type hum1 for h=0 mod 12
AU - Wei, Hengjia
AU - Ge, Gennian
N1 - Funding Information:
Specialized Research Fund for the Doctoral Program of Higher Education. The authors express their gratitude to the two anonymous reviewers for their detailed and constructive comments which are very helpful to the improvement of the technical presentation of this paper.
Funding Information:
Acknowledgments Research supported by the National Outstanding Youth Science Foundation of China under Grant No. 10825103, National Natural Science Foundation of China under Grant No. 61171198, and
PY - 2014/1/1
Y1 - 2014/1/1
N2 - Constructing non-uniform designs has become a topic of considerable interest over the last two decades due to the vital role of such designs in the constructions for other types of designs. Ge, Rees and Shalaby started the investigation into the spectrum of non-uniform Kirkman frames of type h um1. They determined the spectrum for the cases where h ∈ \{2,4,6,8,10,12\, leaving 24 cases of (h,u,m). In this paper, we continue to investigate this spectrum problem by removing all of these 24 possible exceptions. Using this result, we show that for each value of h=0 mod 12the obvious necessary conditions on u, m are also sufficient.
AB - Constructing non-uniform designs has become a topic of considerable interest over the last two decades due to the vital role of such designs in the constructions for other types of designs. Ge, Rees and Shalaby started the investigation into the spectrum of non-uniform Kirkman frames of type h um1. They determined the spectrum for the cases where h ∈ \{2,4,6,8,10,12\, leaving 24 cases of (h,u,m). In this paper, we continue to investigate this spectrum problem by removing all of these 24 possible exceptions. Using this result, we show that for each value of h=0 mod 12the obvious necessary conditions on u, m are also sufficient.
KW - Double group divisible designs
KW - Frames
KW - Group divisible designs
KW - Incomplete group divisible designs
UR - http://www.scopus.com/inward/record.url?scp=84903550704&partnerID=8YFLogxK
U2 - 10.1007/s10623-012-9780-5
DO - 10.1007/s10623-012-9780-5
M3 - Article
AN - SCOPUS:84903550704
SN - 0925-1022
VL - 72
SP - 497
EP - 510
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 3
ER -