Generalised Bhaskar Rao designs with elements from cyclic groups of even order
نویسندگان
چکیده
A necessary condition is given for the existence of some Generalised Bhaskar Rao designs (GBRDs) with odd block size over cyclic groups of even order. Some constructions are given for GBRDs over cyclic groups of even order with block size 3 and with block size 4. AMS Subject Classification: 05B99 J( ey words and phrases: Balanced Incomplete Block Designs; Generalised Bhaskar Rao Designs
منابع مشابه
Bhaskar Rao designs and the groups of order 12
We complete the solution of the existence problem for generalized Bhaskar Rao designs of block size 3 over groups of order 12. In particular we prove that if G is a group of order 12 which is cyclic or dicyclic, then a generalized Bhaskar Rao design, GBRD(v, 3, λ = 12t;G) exists for all v ≥ 3 when t is even and for all v ≥ 4 when t is odd.
متن کاملBhaskar Rao ternary designs and applications
Generalized Bhaskar Rao n-ary are defined. This paper studies with elements from abelian groups of Generalized Bhaskar Rao nary called Bhaskar Rao Bhaskar Rao a v b matrix of ±1 and such that the inner product of any two rows 0 and the matrix obtained of X by its absolute value the incidence matrix of the construction of infinite families of Balanced Balanced are Some construction methods and n...
متن کاملGeneralized Bhaskar Rao designs with two association classes
In previous work generalized Bhaskar Rao designs whose underlying design is a b~lanced incomplete block design have been considered. In the first section of this paper generalized Bhaskar Rao designs (with 2 association classes) whose underlying design is a group divisible design are defin~d. Some methods for the construction of these designs are developed in the second section. It is shown tha...
متن کاملGeneralized Bhaskar Rao designs with block size three
We show that the necessary conditions λ = 0 (mod IGI), λ(v-l)=0 (mod2), λv(v 1) = [0 (mod 6) for IGI odd, (0 (mod 24) for IGI even, are sufficient for the existence of a generalized Bhaskar Rao design GBRD(v,b,r,3,λ;G) for the elementary abelian group G, of each order IGI. Disciplines Physical Sciences and Mathematics Publication Details Seberry, J, Generalized Bhaskar Rao designs with block si...
متن کاملBhaskar Rao designs over small groups
We show that for each of the groups S3, D4, Q4, Z4 x Z2 and D6 the necessary conditions are sufficient for the existence of a generalized Bhaskar Rao design. That is, we show that: (i) a GBRD (v, 3, λ; S3) exists if and only if λ ≡ O (mod 6 ) and λv(v 1) ≡ O(mod 24); (ii) if G is one of the groups D4, Q4, and Z4 x Z2, a GBRD (v, 3, λ; G) exists if and only if λ ≡ O(mod 8) and λv(v 1) ≡ O(mod 6)...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 3 شماره
صفحات -
تاریخ انتشار 1991