Doubly homogeneous 2-(v, k, 1) designs
Journal of Combinatorial Theory Series A
Design theory
Steiner triple systems with an involution
European Journal of Combinatorics
Bicyclic Steiner triple systems
Discrete Mathematics
Steiner triple systems with transrotational automorphisms
Discrete Mathematics
Asymptotically optimal erasure-resilient codes for large disk arrays
Discrete Applied Mathematics - Coding, cryptography and computer security
On 6-sparse Steiner triple systems
Journal of Combinatorial Theory Series A
Combinatorial constructions of low-density parity-check codes for iterative decoding
IEEE Transactions on Information Theory
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In 1973 Paul Erd驴s conjectured that there is an integer v 0(r) such that, for every vv 0(r) and v驴1,3 (mod 6), there exists a Steiner triple system of order v, containing no i blocks on i+2 points for every 1i驴r. Such an STS is said to be r-sparse. In this paper we consider relations of automorphisms of an STS to its sparseness. We show that for every r驴13 there exists no point-transitive r-sparse STS over an abelian group. This bound and the classification of transitive groups give further nonexistence results on block-transitive, flag-transitive, 2-transitive, and 2-homogeneous STSs with high sparseness. We also give stronger bounds on the sparseness of STSs having some particular automorphisms with small groups. As a corollary of these results, it is shown that various well-known automorphisms, such as cyclic, 1-rotational over arbitrary groups, and involutions, prevent an STS from being high-sparse.