Constructions of uniform designs by using resolvable packings and coverings
نویسندگان
چکیده
In this paper, uniform designs are constructed based on nearly U-type designs and the discrete discrepancy. The link between such uniform designs and resolvable packings and coverings in combinatorial design theory is developed. Through resolvable packings and coverings without identical parallel classes, many infinite classes of new uniform designs are then produced.
منابع مشابه
Maximal Resolvable Packings and Minimal Resolvable Coverings of Triples by Quadruples
Determination of maximal resolvable packing number and minimal resolvable covering number is a fundamental problem in designs theory. In this article, we investigate the existence of maximal resolvable packings of triples by quadruples of order v (MRPQS(v)) and minimal resolvable coverings of triples by quadruples of order v (MRCQS(v)). We show that an MRPQS(v) (MRCQS(v)) with the number of blo...
متن کاملResolvable packings R̃ MP ( 3 , 2 ; n , n − 3 ) and coverings R̃ MC ( 3 , 2 ; n , n − 2 )
Letn ≡ k−1, 0 or 1 (mod k).An R̃MP(k, ; n,m) (resp. R̃MC(k, ; n,m)) is a resolvable packing (resp. covering)withmaximum (resp. minimum) possible number m of parallel classes which are mutually distinct, each parallel class consists of (n− k + 1)/k blocks of size k and one block of size n− k (n− k+ 1)/k , and its leave (resp. excess) is a simple graph. Such designs can be used to construct certain...
متن کاملUniform Designs and Their Combinatorial Constructions
Uniform designs has been widely used in various fields. In this talk, two constructions for uniform designs from combinatorics are presented. One is obtained by resolvable PPBDs which serves to unify some known combinatorial constructions. The other provides a recursive method to obtain a new three-level uniform design from old one.
متن کاملInvited Talks
In 2009, Peter Cameron introduced a common generalization of various classes of combinatorial designs such as balanced incomplete block designs, resolvable designs and orthogonal arrays. Generalized covering and packing designs can be defined in analogous way. These objects bring into this framework further classes of designs, including covering and packing arrays, Howell designs, monogamous cy...
متن کاملConstructions for Key Distribution Pattern using Resolvable Designs
Key distribution patterns (KDPs) are finite incidence structures satisfying a certain property which makes them widely used in minimizing the key storage and ensuring the security of communication between users in a large network. In this paper we discuss the close connection between resolvable designs and KDPs, and convert the constructions of KDPs into the constructions of resolvable designs....
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:
- Discrete Mathematics
دوره 274 شماره
صفحات -
تاریخ انتشار 2004