Super-simple 2-(v, 5, 1) directed designs and their smallest defining sets
نویسندگان
چکیده
In this paper we investigate the spectrum of super-simple 2-(v, 5, 1) directed designs (or simply super-simple 2-(v, 5, 1)DDs) and also the size of their smallest defining sets. We show that for all v ≡ 1, 5 (mod 10) except v = 5, 15 there exists a super-simple (v, 5, 1)DD. Also for these parameters, except possibly v = 11, 91, there exists a super-simple 2-(v, 5, 1)DD whose smallest defining sets have at least a half of the blocks.
منابع مشابه
On Minimal Defining Sets of Full Designs and Self-Complementary Designs, and a New Algorithm for Finding Defining Sets of t-Designs
A defining set of a t-(v, k, λ) design is a partial design which is contained in a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper partial designs is a defining set. This paper proposes a new and more efficient algorithm that finds all non-isomorphic minimal defining sets of a given t-design. The complete list of minimal defining sets of...
متن کاملOn defining sets of directed designs
The concept of defining set has been studied in block designs and, under the name critical sets, in Latin squares and Room squares. Here we study defining sets for directed designs. A t-(v, k,'x) directed design (DD) is a pair (V, B), where V is a v-set and B is a collection of ordered blocks (or k-tuples of V), for which each t-tuple of V appears in precisely ,X blocks. A set of blocks which i...
متن کاملSmallest defining sets for 2-(9, 4, 3) and 3-(10, 5, 3) designs
A set of blocks which can be completed to exactly one t-(v, k, A) design is called a defining set of that design. A known algorithm is used to determine all smallest defining sets of the 11 non-isomorphic 2-(9,4,3) designs. Nine of the designs have smallest defining sets of eight blocks each; the other two have smallest defining sets of six blocks each. Various methods are then used to find all...
متن کاملOn The Spectrum of Minimal Defining Sets of Full Designs
A defining set of a t-(v,k,λ ) design is a subcollection of the block set of the design which is not contained in any other design with the same parameters. A defining set is said to be minimal if none of its proper subcollections is a defining set. A defining set is said to be smallest if no other defining set has a smaller cardinality. A t-(v,k,λ ) design D = (V,B) is called a full design if ...
متن کاملOn Defining Sets of Full Designs with Block Size Three
A defining set of a t-(v, k, λ) design is a subcollection of its blocks which is contained in no other t-design with the given parameters, on the same point set. A minimal defining set is a defining set, none of whose proper subcollections is a defining set. The spectrum of minimal defining sets of a design D is the set {|M | | M is a minimal defining set of D}. We show that if a t-(v, k, λ) de...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Australasian J. Combinatorics
دوره 54 شماره
صفحات -
تاریخ انتشار 2012