Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems
نویسندگان
چکیده
منابع مشابه
Minimal defining sets in a family of Steiner triple systems
A defining set of a block design is a subset of the blocks of the design which are a subset of no other design with the same parameters. This paper describes and proves the existence of a certain type of set of blocks in the infinite family of Steiner triple systems isomorphic to the points and lines of the projective geometries over GF(2). It is then proven that these sets of blocks are defini...
متن کاملSets of three pairwise orthogonal Steiner triple systems
Two Steiner triple systems (STS) are orthogonal if their sets of triples are disjoint, and two disjoint pairs of points defining intersecting triples in one system fail to do so in the other. In 1994, it was shown [2] that there exist a pair of orthogonal Steiner triple systems of order v for all v ≡ 1, 3 (mod 6), with v ≥ 7, v 6= 9. In this paper we show that there exist three pairwise orthogo...
متن کاملOn large sets of v − 1 L - intersecting Steiner triple systems of order
This paper presents four new recursive constructions for large sets of v − 1 STS(v). These facilitate the production of several new infinite families of such large sets. In particular, we obtain for each n ≥ 2 a large set of 3 − 1 STS(3) whose systems intersect in 0 or 3 blocks.
متن کاملOn Large Sets of v-1 L-Intersecting Steiner Triple Systems of Order v
This paper presents four new recursive constructions for large sets of v − 1 STS(v). These facilitate the production of several new infinite families of such large sets. In particular, we obtain for each n ≥ 2 a large set of 3 − 1 STS(3) whose systems intersect in 0 or 3 blocks.
متن کامل5-sparse Steiner Triple Systems of Order n Exist for Almost All Admissible n
Steiner triple systems are known to exist for orders n ≡ 1, 3 mod 6, the admissible orders. There are many known constructions for infinite classes of Steiner triple systems. However, Steiner triple systems that lack prescribed configurations are harder to find. This paper gives a proof that the spectrum of orders of 5-sparse Steiner triple systems has arithmetic density 1 as compared to the ad...
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:
- Graphs and Combinatorics
دوره 19 شماره
صفحات -
تاریخ انتشار 2003