Towards a Large Set of Steiner Quadruple Systems
نویسندگان
چکیده
منابع مشابه
The existence of resolvable Steiner quadruple systems
A Steiner quadruple system of order v is a set X of cardinality v, and a set Q, of 4-subsets of X, called blocks, with the property that every 3-subset of X is contained in a unique block. A Steiner quadruple system is resolvable if Q can be partitioned into parallel classes (partitions of X). A necessary condition for the existence of a resolvable Steiner quadruple system is that v = 4 or 8 (m...
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The upper chromatic number χ(H) of a set system H is the maximum number of colours that can be assigned to the elements of the underlying set of H in such a way that each H ∈ H contains a monochromatic pair of elements. We prove that a Steiner Triple System of order v ≤ 2 − 1 has an upper chromatic number which is at most k. This bound is the best possible, and the extremal configurations attai...
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A Steiner quadruple system (X, B) is said to be (1, 2)-resolvable if its blocks can be partitioned into r parts such that each point of X occurs in exactly two blocks in each part. The necessary condition for the existence of (1, 2)-resolvable Steiner quadruple systems RSQS(1, 2, v)s is v ≡ 2 or 10 (mod 12). Hartman and Phelps in [A. Hartman, K.T. Phelps, Steiner quadruple systems, in: J.H. Din...
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Let N = Ln(q), n ≥ 2, q a prime power, be a projective linear simple group. We classify all Steiner quadruple systems admitting a group G with N ≤ G ≤ Aut(N). In particular, we show that G cannot act as a group of automorphisms on any Steiner quadruple system for n > 2.
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A singular direct product construction is presented for Steiner quadruple systems with a spanning block design. More constructions are also provided using Steiner systems S(3; k; v) and other designs. Small orders for v = 40 and 52 are constructed directly. Some in1nite classes of orders are also obtained. c © 2002 Elsevier Science B.V. All rights reserved.
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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 4 شماره
صفحات -
تاریخ انتشار 1991